Collectanea Mathematica最新文献

{"title":"Infinitely many positive energy solutions for semilinear Neumann equations with critical Sobolev exponent and concave-convex nonlinearity","authors":"Rachid Echarghaoui, Rachid Sersif, Zakaria Zaimi","doi":"10.1007/s13348-023-00426-4","DOIUrl":"https://doi.org/10.1007/s13348-023-00426-4","url":null,"abstract":"<p>The authors of Cao and Yan (J Differ Equ 251:1389–1414, 2011) have considered the following semilinear critical Neumann problem </p><span>$$begin{aligned} varvec{-Delta u=vert uvert ^{2^{*}-2} u+g(u) quad text{ in } Omega , quad frac{partial u}{partial nu }=0 quad text{ on } partial Omega ,} end{aligned}$$</span><p>where <span>(varvec{Omega })</span> is a bounded domain in <span>(varvec{mathbb {R}^{N}})</span> satisfying some geometric conditions, <span>(varvec{nu })</span> is the outward unit normal of <span>(varvec{partial Omega , 2^{*}:=frac{2 N}{N-2}})</span> and <span>(varvec{g(t):=mu vert tvert ^{p-2} t-t,})</span> where <span>(varvec{p in left( 2,2^{*}right) })</span> and <span>(varvec{mu &gt;0})</span> are constants. They proved the existence of infinitely many solutions with positive energy for the above problem if <span>(varvec{N&gt;max left( frac{2(p+1)}{p-1}, 4right) .})</span> In this present paper, we consider the case where the exponent <span>(varvec{p in left( 1,2right) })</span> and we show that if <span>(varvec{N&gt;frac{2(p+1)}{p-1},})</span> then the above problem admits an infinite set of solutions with positive energy. Our main result extend that obtained by P. Han in [9] for the case of elliptic problem with Dirichlet boundary conditions.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Maximal operators on hyperbolic triangles","authors":"Romain Branchereau, Samuel Bronstein, Anthony Gauvan","doi":"10.1007/s13348-023-00419-3","DOIUrl":"https://doi.org/10.1007/s13348-023-00419-3","url":null,"abstract":"<p>We characterize the boundedness properties on the spaces <span>(L^p( mathbb {H}^2))</span> of the maximal operator <span>(M_mathcal {B})</span> where <span>(mathcal {B})</span> is an arbitrary family of hyperbolic triangles stable by isometries. </p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cofiniteness of local cohomology modules and subcategories of modules","authors":"Ryo Takahashi, Naoki Wakasugi","doi":"10.1007/s13348-023-00416-6","DOIUrl":"https://doi.org/10.1007/s13348-023-00416-6","url":null,"abstract":"<p>Let <i>R</i> be a commutative noetherian ring and <i>I</i> an ideal of <i>R</i>. Assume that for all integers <i>i</i> the local cohomology module <span>({text {H}}_I^i(R))</span> is <i>I</i>-cofinite. Suppose that <span>(R_mathfrak {p})</span> is a regular local ring for all prime ideals <span>(mathfrak {p})</span> that do not contain <i>I</i>. In this paper, we prove that if the <i>I</i>-cofinite modules form an abelian category, then for all finitely generated <i>R</i>-modules <i>M</i> and all integers <i>i</i>, the local cohomology module <span>({text {H}}_I^i(M))</span> is <i>I</i>-cofinite.\u0000</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the interior Bernoulli free boundary problem for the fractional Laplacian on an interval","authors":"Tadeusz Kulczycki, Jacek Wszoła","doi":"10.1007/s13348-023-00417-5","DOIUrl":"https://doi.org/10.1007/s13348-023-00417-5","url":null,"abstract":"Abstract We study the structure of solutions of the interior Bernoulli free boundary problem for $$(-Delta )^{alpha /2}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> on an interval D with parameter $$lambda &gt; 0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . In particular, we show that there exists a constant $$lambda _{alpha ,D} &gt; 0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> (called the Bernoulli constant) such that the problem has no solution for $$lambda in (0,lambda _{alpha ,D})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , at least one solution for $$lambda = lambda _{alpha ,D}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and at least two solutions for $$lambda &gt; lambda _{alpha ,D}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . We also study the interior Bernoulli problem for the fractional Laplacian for an interval with one free boundary point. We discuss the connection of the Bernoulli problem with the corresponding variational problem and present some conjectures. In particular, we show for $$alpha = 1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> that there exists solutions of the interior Bernoulli free boundary problem for $$(-Delta )^{alpha /2}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> on an interval which are not minimizers of the corresponding variational problem.","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135391562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Skew derivations of incidence algebras","authors":"Érica Z. Fornaroli, Mykola Khrypchenko","doi":"10.1007/s13348-023-00423-7","DOIUrl":"https://doi.org/10.1007/s13348-023-00423-7","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135773670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Refined two weight estimates for the Bergman projection","authors":"Gianmarco Brocchi","doi":"10.1007/s13348-023-00420-w","DOIUrl":"https://doi.org/10.1007/s13348-023-00420-w","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Lipschitz numerical index of Banach spaces","authors":"Geunsu Choi, Mingu Jung, Hyung-Joon Tag","doi":"10.1007/s13348-023-00421-9","DOIUrl":"https://doi.org/10.1007/s13348-023-00421-9","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Attractor for minimal iterated function systems","authors":"Aliasghar Sarizadeh","doi":"10.1007/s13348-023-00422-8","DOIUrl":"https://doi.org/10.1007/s13348-023-00422-8","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Disjoint hypercyclic and supercyclic composition operators on discrete weighted Banach spaces","authors":"Zhiyuan Xu, Ya Wang, Zehua Zhou","doi":"10.1007/s13348-023-00418-4","DOIUrl":"https://doi.org/10.1007/s13348-023-00418-4","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135512915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Morelli-Włodarczyk cobordism and examples of rooftop flips","authors":"Lorenzo Barban, Alberto Franceschini","doi":"10.1007/s13348-023-00415-7","DOIUrl":"https://doi.org/10.1007/s13348-023-00415-7","url":null,"abstract":"Abstract We introduce the notion of rooftop flip, namely a small modification among normal projective varieties which is modeled by a smooth projective variety of Picard number 2 admitting two projective bundle structures. Examples include the Atiyah flop and the Mukai flop, modeled respectively by $$mathbb {P}^1times mathbb {P}^1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:math> and by $$mathbb {P}left( T_{mathbb {P}^2}right) $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>T</mml:mi> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:msub> </mml:mfenced> </mml:mrow> </mml:math> . Using the Morelli-Włodarczyk cobordism, we prove that any smooth projective variety of Picard number 1, endowed with a $${mathbb C}^*$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -action with only two fixed point components, induces a rooftop flip.","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135060768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}