Bulletin des Sciences Mathematiques最新文献

{"title":"Bilinear singular integral operators with generalized kernels and their commutators on product of (grand) generalized fractional (weighted) Morrey spaces","authors":"Guanghui Lu, Miaomiao Wang, Shuangping Tao, Ronghui Liu","doi":"10.1016/j.bulsci.2024.103544","DOIUrl":"10.1016/j.bulsci.2024.103544","url":null,"abstract":"<div><div>The purpose of this article is to establish the boundedness of a bilinear singular integral operator <span><math><mover><mrow><mi>T</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> with generalized kernels and its commutator <span><math><msub><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub></math></span> formed by <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mrow><mi>BMO</mi></mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> and the <span><math><mover><mrow><mi>T</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> on product of generalized fractional Morrey spaces <span><math><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mi>φ</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>η</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>φ</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, product of generalized fractional weighted Morrey spaces <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mi>φ</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>×</mo><msubsup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>η</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>φ</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> and product of grand generalized fractional weighted Morrey spaces <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>,</mo><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mi>φ</mi><mo>,</mo><mi>θ</mi><mo>,</mo><mi>σ</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>×</mo><msubsup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>,</mo><m","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103544"},"PeriodicalIF":1.3,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143173034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bézier curves and the Takagi function","authors":"Lenka Ptáčková ,&nbsp;Franco Vivaldi","doi":"10.1016/j.bulsci.2024.103543","DOIUrl":"10.1016/j.bulsci.2024.103543","url":null,"abstract":"<div><div>We consider Bézier curves with complex parameters, and we determine explicitly the affine iterated function system (IFS) corresponding to the de Casteljau subdivision algorithm, together with the complex parametric domain over which such an IFS has a unique global connected attractor. For a specific family of complex parameters having vanishing imaginary part, we prove that the Takagi fractal curve is the attractor, under suitable scaling.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103543"},"PeriodicalIF":1.3,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the moduli space of simple sheaves on singular K3 surfaces","authors":"Barbara Fantechi ,&nbsp;Rosa M. Miró-Roig","doi":"10.1016/j.bulsci.2024.103540","DOIUrl":"10.1016/j.bulsci.2024.103540","url":null,"abstract":"<div><div>Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in <span><span>[6]</span></span> we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones. In this paper, we extend both Mukai's result and our construction to reduced projective K3 surfaces; for the former we need to restrict our attention to perfect sheaves. There are two key points where we cannot get a straightforward generalization. In each, we need to prove that a certain differential form on the moduli space of simple, perfect sheaves vanishes, and we introduce a smoothability condition to complete the proof.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103540"},"PeriodicalIF":1.3,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Representability of G-functions as rational functions in hypergeometric series","authors":"T. Dreyfus ,&nbsp;T. Rivoal","doi":"10.1016/j.bulsci.2024.103542","DOIUrl":"10.1016/j.bulsci.2024.103542","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Fresán and Jossen have given a negative answer to a question of Siegel about the representability of every &lt;em&gt;E&lt;/em&gt;-function as a polynomial with algebraic coefficients in &lt;em&gt;E&lt;/em&gt;-functions of type &lt;span&gt;&lt;math&gt;&lt;mmultiscripts&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;none&gt;&lt;/none&gt;&lt;mprescripts&gt;&lt;/mprescripts&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;none&gt;&lt;/none&gt;&lt;/mmultiscripts&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;_&lt;/mo&gt;&lt;/munder&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;_&lt;/mo&gt;&lt;/munder&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt; and rational parameters &lt;span&gt;&lt;math&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;_&lt;/mo&gt;&lt;/munder&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;_&lt;/mo&gt;&lt;/munder&gt;&lt;/math&gt;&lt;/span&gt;. In this paper, we study, in a more general context, a similar question for &lt;em&gt;G&lt;/em&gt;-functions asked by Fischler and the second author: can every &lt;em&gt;G&lt;/em&gt;-function be represented as a polynomial with algebraic coefficients in &lt;em&gt;G&lt;/em&gt;-functions of type &lt;span&gt;&lt;math&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;_&lt;/mo&gt;&lt;/munder&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;_&lt;/mo&gt;&lt;/munder&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, rational parameters &lt;span&gt;&lt;math&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;_&lt;/mo&gt;&lt;/munder&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;munder&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;_&lt;/mo&gt;&lt;/munder&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; algebraic over &lt;span&gt;&lt;math&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;? They have shown the answer to be negative under a generalization of Grothendieck's Period Conjecture and a technical assumption on the &lt;em&gt;λ&lt;/em&gt;'s. Using differential Galois theory, we prove that, for every &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, there exists a &lt;em&gt;G&lt;/em&gt;-function which can not be represented as a rational function with coefficients in &lt;span&gt;&lt;math&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt; of solutions of linear differential equations with coefficients in &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and at most &lt;em&gt;N&lt;/em&gt; singularities in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. As a corollary, we deduce that not all &lt;em&gt;G&lt;/em&gt;-functions can be represented as a rational function in hypergeometric series of the above mentioned","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103542"},"PeriodicalIF":1.3,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143173036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global strong solutions to nonlocal Benjamin-Bona-Mahony equations with exponential nonlinearities","authors":"Nguyen Huy Tuan ,&nbsp;Bui Dai Nghia ,&nbsp;Nguyen Anh Tuan","doi":"10.1016/j.bulsci.2024.103539","DOIUrl":"10.1016/j.bulsci.2024.103539","url":null,"abstract":"<div><div>In the current work, we consider the Cauchy problem for a class of adjusted Benjamin-Bona-Mahony (BBM) equations. These equations are modified by considering the time-fractional Caputo derivative of order <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> (instead of the classical one) and an additional nonlinearity of exponential type. The first main result includes the unique global existence of strong solutions. The approach for this goal can be summarized as follows. First of all, we use the standard contraction arguments to prove the local existence and uniqueness of a mild solution. Next, apply a weak version of Grönwall's inequality to improve the temporal regularity of the solutions. Using this regularity, we deduce energy estimates for solutions which helps us to obtain the global boundedness. The second aim of the study is about the behavior of solutions according to the fractional order <em>α</em>. Precisely, we show that our solutions converge to those of the classical model (with integer order derivative) as <em>α</em> approaches <span><math><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math></span>. The desired result is derived by some singular integral estimates which is the combination of some essential basic inequalities.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103539"},"PeriodicalIF":1.3,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143173037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiplicity of solutions for a class of new p(x)-Kirchhoff problem","authors":"Chunbo Lian ,&nbsp;Bin Ge ,&nbsp;Lijiang Jia","doi":"10.1016/j.bulsci.2024.103537","DOIUrl":"10.1016/j.bulsci.2024.103537","url":null,"abstract":"<div><div>The nonlocal <span><math><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>-Kirchhoff equations without the Ambrosetti-Rabinowitz type condition are considered in this paper. Under very weak assumptions on the nonlinear term <em>g</em>, we establish some results about the existence of nontrivial solutions by using variational methods. In addition, we also study the existence of infinitely many solutions for even energy functional. Our results can be viewed as the improvement, supplementation and extension of the corresponding results obtained by Hamdani et al. (2020).</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"198 ","pages":"Article 103537"},"PeriodicalIF":1.3,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a generalization of a result of Howe for unipotent groups","authors":"Souha Maaref","doi":"10.1016/j.bulsci.2024.103536","DOIUrl":"10.1016/j.bulsci.2024.103536","url":null,"abstract":"<div><div>Let <em>F</em> be a nonarchimedean local field of characteristic zero and <strong>G</strong> be a unipotent algebraic group defined over <em>F</em>. The set of rational points of <strong>G</strong>, denoted by <em>G</em>, is a <em>p</em>-adic Lie group. Let <span><math><mi>g</mi></math></span> be the Lie algebra of <em>G</em>. Now let <em>H</em> be a normal closed subgroup of <em>G</em>, <em>χ</em> be a unitary character of <em>H</em> and <em>π</em> be an irreducible unitary representation of <em>G</em> in a Hilbert space <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>π</mi></mrow></msub></math></span>. The aim of this paper is the determination of the space formed by the <em>χ</em>-semi-invariant vectors of <em>π</em>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"198 ","pages":"Article 103536"},"PeriodicalIF":1.3,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Holomorphic one-parameter semigroups of bounded linear operators on Lp(Rn), 1 < p < ∞, generated by strongly M-elliptic pseudo-differential operators","authors":"Yaodong Gao,&nbsp;M.W. Wong","doi":"10.1016/j.bulsci.2024.103535","DOIUrl":"10.1016/j.bulsci.2024.103535","url":null,"abstract":"<div><div>For a <em>M</em>-elliptic pseudo-differential operator on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, we give a sufficient condition on its symbol to ensure that it is the infinitesimal generator of a holomorphic one-parameter semigroup of bounded linear operators on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"198 ","pages":"Article 103535"},"PeriodicalIF":1.3,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition","authors":"Eleonora Amoroso ,&nbsp;Ángel Crespo-Blanco ,&nbsp;Patrizia Pucci ,&nbsp;Patrick Winkert","doi":"10.1016/j.bulsci.2024.103534","DOIUrl":"10.1016/j.bulsci.2024.103534","url":null,"abstract":"<div><div>In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness of the solutions of a wide class of nonlinear Neumann problems, both of independent interest. Moreover, we study a variable exponent double phase problem with a nonlinear boundary condition and prove the existence of multiple solutions under very general assumptions on the nonlinearities. To be more precise, we get constant sign solutions (nonpositive and nonnegative) via a mountain-pass approach and a sign-changing solution by using an appropriate subset of the corresponding Nehari manifold along with the Brouwer degree and the Quantitative Deformation Lemma.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"197 ","pages":"Article 103534"},"PeriodicalIF":1.3,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Liouville theorems for Choquard-Pekar equations on the half space","authors":"Huxiao Luo ,&nbsp;Yating Xu","doi":"10.1016/j.bulsci.2024.103533","DOIUrl":"10.1016/j.bulsci.2024.103533","url":null,"abstract":"<div><div>We study the following Dirichlet problem to the Choquard-Pekar equation<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd></mtd><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mrow><mo>(</mo><munder><mo>∫</mo><mrow><mi>Ω</mi></mrow></munder><mfrac><mrow><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>n</mi><mo>−</mo><mi>β</mi></mrow></msup></mrow></mfrac><mi>d</mi><mi>y</mi><mo>)</mo></mrow><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≡</mo><mn>0</mn><mo>,</mo><mspace></mspace><mi>x</mi><mo>∉</mo><mi>Ω</mi><mo>.</mo></mtd></mtr></mtable></mrow></math></span></span></span> For <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mi>β</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math></span>, <span><math><mn>1</mn><mo>≤</mo><mi>q</mi><mo>≤</mo><mfrac><mrow><mn>2</mn><mo>+</mo><mi>β</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math></span> and <span><math><mi>Ω</mi><mo>=</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>, we prove the non-existence of non-negative solutions by the method of moving planes. As an application of the Liouville theorem in half space and the Liouville theorem in whole space obtained in <span><span>[13]</span></span>, <span><span>[28]</span></span>, we carry on blowing-up and rescaling argument on the Choquard-Pekar equation in a bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, and thus obtain a priori estimates on the positive solutions. Based on this estimate and the Leray-Schauder degree theory, we establish the existence of positive solutions.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"197 ","pages":"Article 103533"},"PeriodicalIF":1.3,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}