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Corrigendum to “Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness” [Nonlinear Anal. 101 (2014) 98–112] “具有有限平滑的多线性和多参数傅立叶乘子算子的Hörmander型定理”的更正[非线性分析]. 101 (2014)98-112]
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-03 DOI: 10.1016/j.na.2025.113750
Jiao Chen , Guozhen Lu
{"title":"Corrigendum to “Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness” [Nonlinear Anal. 101 (2014) 98–112]","authors":"Jiao Chen , Guozhen Lu","doi":"10.1016/j.na.2025.113750","DOIUrl":"10.1016/j.na.2025.113750","url":null,"abstract":"","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113750"},"PeriodicalIF":1.3,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163863","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}
引用次数: 0
Local uniqueness of minimizers for Choquard type equations Choquard型方程最小解的局部唯一性
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-03 DOI: 10.1016/j.na.2025.113764
Lintao Liu , Kaimin Teng , Shuai Yuan
{"title":"Local uniqueness of minimizers for Choquard type equations","authors":"Lintao Liu ,&nbsp;Kaimin Teng ,&nbsp;Shuai Yuan","doi":"10.1016/j.na.2025.113764","DOIUrl":"10.1016/j.na.2025.113764","url":null,"abstract":"<div><div>We consider <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-constraint minimizers of the Choquard energy functional with a trapping potential <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>. It is known that positive minimizers exist if and only if the parameter <span><math><mi>a</mi></math></span> satisfies <span><math><mrow><mi>a</mi><mo>&lt;</mo><msup><mrow><mi>a</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>≔</mo><msubsup><mrow><mo>‖</mo><mi>Q</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math></span>, where <span><math><mi>Q</mi></math></span> is the unique positive radial solution of <span><math><mrow><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>−</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. This paper focuses on the local uniqueness of minimizers by using energy estimates, blow-up analysis and establishing the Pohozăev identity.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113764"},"PeriodicalIF":1.3,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163859","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}
引用次数: 0
Fujita exponent and blow-up rate for a mixed local and nonlocal heat equation 局部和非局部混合热方程的Fujita指数和爆破率
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-03 DOI: 10.1016/j.na.2025.113761
Leandro M. Del Pezzo , Raúl Ferreira
{"title":"Fujita exponent and blow-up rate for a mixed local and nonlocal heat equation","authors":"Leandro M. Del Pezzo ,&nbsp;Raúl Ferreira","doi":"10.1016/j.na.2025.113761","DOIUrl":"10.1016/j.na.2025.113761","url":null,"abstract":"<div><div>In this paper we consider the blow-up problem for a mixed local-nonlocal diffusion operator, <span><span><span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>a</mi><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>b</mi><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></math></span></span></span>We show that the Fujita exponent is given by the nonlocal part, <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>=</mo><mn>1</mn><mo>+</mo><mn>2</mn><mi>s</mi><mo>/</mo><mi>N</mi></mrow></math></span>. We also determinate, in some cases, the blow-up rate.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113761"},"PeriodicalIF":1.3,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162489","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}
引用次数: 0
Extremal functions for twisted sharp Sobolev inequalities with lower order remainder terms 具有低阶余项的扭曲尖锐Sobolev不等式的极值函数
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-02-01 DOI: 10.1016/j.na.2025.113758
Olivier Druet , Emmanuel Hebey
{"title":"Extremal functions for twisted sharp Sobolev inequalities with lower order remainder terms","authors":"Olivier Druet ,&nbsp;Emmanuel Hebey","doi":"10.1016/j.na.2025.113758","DOIUrl":"10.1016/j.na.2025.113758","url":null,"abstract":"<div><div>We prove existence of extremal functions and compactness of the set of extremal functions for twisted sharp 4-dimensional Sobolev inequalities with lower order remainder terms.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113758"},"PeriodicalIF":1.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162490","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}
引用次数: 0
Universal differentiability sets in Laakso space Laakso空间中的全称可微集
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-01-31 DOI: 10.1016/j.na.2025.113752
Sylvester Eriksson-Bique , Andrea Pinamonti , Gareth Speight
{"title":"Universal differentiability sets in Laakso space","authors":"Sylvester Eriksson-Bique ,&nbsp;Andrea Pinamonti ,&nbsp;Gareth Speight","doi":"10.1016/j.na.2025.113752","DOIUrl":"10.1016/j.na.2025.113752","url":null,"abstract":"<div><div>We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal differentiability set in Laakso space. Additionally, we show that each of the measures constructed supports a Poincaré inequality.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113752"},"PeriodicalIF":1.3,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162487","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}
引用次数: 0
Semiclassical states for the curl–curl problem 旋旋问题的半经典态
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-01-31 DOI: 10.1016/j.na.2025.113756
Bartosz Bieganowski , Adam Konysz , Jarosław Mederski
{"title":"Semiclassical states for the curl–curl problem","authors":"Bartosz Bieganowski ,&nbsp;Adam Konysz ,&nbsp;Jarosław Mederski","doi":"10.1016/j.na.2025.113756","DOIUrl":"10.1016/j.na.2025.113756","url":null,"abstract":"<div><div>We show the existence of the so-called semiclassical states <span><math><mrow><mi>U</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span> to the following curl–curl problem <span><math><mrow><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>2</mn></mrow></msup><mspace></mspace><mo>∇</mo><mo>×</mo><mrow><mo>(</mo><mo>∇</mo><mo>×</mo><mi>U</mi><mo>)</mo></mrow><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>U</mi><mo>=</mo><mi>g</mi><mrow><mo>(</mo><mi>U</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span> for sufficiently small <span><math><mrow><mi>ɛ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. We study the asymptotic behaviour of solutions as <span><math><mrow><mi>ɛ</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math></span> and we investigate also a related nonlinear Schrödinger equation involving a singular potential. The problem models large permeability nonlinear materials satisfying the system of Maxwell equations.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113756"},"PeriodicalIF":1.3,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163864","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}
引用次数: 0
Radial positive solutions for mixed local and nonlocal supercritical Neumann problem 混合局部和非局部超临界Neumann问题的径向正解
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-01-31 DOI: 10.1016/j.na.2025.113763
David Amundsen, Abbas Moameni, Remi Yvant Temgoua
{"title":"Radial positive solutions for mixed local and nonlocal supercritical Neumann problem","authors":"David Amundsen,&nbsp;Abbas Moameni,&nbsp;Remi Yvant Temgoua","doi":"10.1016/j.na.2025.113763","DOIUrl":"10.1016/j.na.2025.113763","url":null,"abstract":"<div><div>In this paper, we establish the existence of positive non-decreasing radial solutions for a nonlinear mixed local and nonlocal Neumann problem in the ball. No growth assumption on the nonlinearity is required. We also provide a criterion for the existence of non-constant solutions provided the problem possesses a trivial constant solution.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113763"},"PeriodicalIF":1.3,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163865","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}
引用次数: 0
Gradient Einstein-type warped products: Rigidity, existence and nonexistence results via a nonlinear PDE 梯度爱因斯坦型翘曲产物：通过非线性偏微分方程得到的刚性、存在性和不存在性结果
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-01-30 DOI: 10.1016/j.na.2025.113759
José Nazareno Vieira Gomes , Willian Isao Tokura
{"title":"Gradient Einstein-type warped products: Rigidity, existence and nonexistence results via a nonlinear PDE","authors":"José Nazareno Vieira Gomes ,&nbsp;Willian Isao Tokura","doi":"10.1016/j.na.2025.113759","DOIUrl":"10.1016/j.na.2025.113759","url":null,"abstract":"<div><div>We establish the necessary and sufficient conditions for constructing gradient Einstein-type warped metrics. One of these conditions leads us to a general Lichnerowicz equation with analytic and geometric coefficients for this class of metrics on the space of warping functions. In this way, we prove gradient estimates for positive solutions of a nonlinear elliptic differential equation on a complete Riemannian manifold with associated Bakry–Émery Ricci tensor bounded from below. As an application, we provide nonexistence and rigidity results for a large class of gradient Einstein-type warped metrics. Furthermore, we show how to construct gradient Einstein-type warped metrics, and then we give explicit examples which are not only meaningful in their own right, but also help to justify our results.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113759"},"PeriodicalIF":1.3,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163860","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}
引用次数: 0
Asymptotics for positive singular solutions to subcritical sixth order equations 次临界六阶方程正奇异解的渐近性
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-01-30 DOI: 10.1016/j.na.2025.113757
João Henrique Andrade , Juncheng Wei
{"title":"Asymptotics for positive singular solutions to subcritical sixth order equations","authors":"João Henrique Andrade ,&nbsp;Juncheng Wei","doi":"10.1016/j.na.2025.113757","DOIUrl":"10.1016/j.na.2025.113757","url":null,"abstract":"<div><div>We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. First, using a version of the integral moving spheres technique, we prove that solutions are asymptotically radially symmetric solutions with respect to the origin. We divide our approach into some cases concerning the growth of nonlinearity. In general, we use an Emden–Fowler change of variables to translate our problem to a cylinder. In the lower critical regime, this is not enough, thus, we need to introduce a new notion of change of variables. The main difficulty is that the cylindrical PDE in this coordinate system is nonautonomous. Nonetheless, we define an associated nonautonomous Pohozaev functional, which can be proved to be asymptotically monotone. In addition, we show <em>a priori</em> estimates for these two functionals, from which we extract compactness properties. With these ingredients, we can perform an asymptotic analysis technique to prove our main result.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113757"},"PeriodicalIF":1.3,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163861","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}
引用次数: 0
Examples of optimal Hölder regularity in semilinear equations involving the fractional Laplacian 涉及分数阶拉普拉斯式的半线性方程中最优Hölder正则性的例子
IF 1.3 2区 数学
Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-01-30 DOI: 10.1016/j.na.2025.113755
Gyula Csató , Albert Mas
{"title":"Examples of optimal Hölder regularity in semilinear equations involving the fractional Laplacian","authors":"Gyula Csató ,&nbsp;Albert Mas","doi":"10.1016/j.na.2025.113755","DOIUrl":"10.1016/j.na.2025.113755","url":null,"abstract":"<div><div>We discuss the Hölder regularity of solutions to the semilinear equation involving the fractional Laplacian <span><math><mrow><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> in one dimension. We put in evidence a new regularity phenomenon which is a combined effect of the nonlocality and the semilinearity of the equation, since it does not happen neither for local semilinear equations, nor for nonlocal linear equations. Namely, for nonlinearities <span><math><mi>f</mi></math></span> in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>β</mi></mrow></msup></math></span> and when <span><math><mrow><mn>2</mn><mi>s</mi><mo>+</mo><mi>β</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the solution is not always <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>s</mi><mo>+</mo><mi>β</mi><mo>−</mo><mi>ϵ</mi></mrow></msup></math></span> for all <span><math><mrow><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. Instead, in general the solution <span><math><mi>u</mi></math></span> is at most <span><math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>s</mi><mo>/</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>β</mi><mo>)</mo></mrow></mrow></msup><mo>.</mo></mrow></math></span></div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113755"},"PeriodicalIF":1.3,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163862","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}
引用次数: 0
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