Advances in Nonlinear Analysis最新文献_第9页

Bounded solutions to systems of fractional discrete equations 分数阶离散方程系统的有界解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0260

J. Diblík

{"title":"Bounded solutions to systems of fractional discrete equations","authors":"J. Diblík","doi":"10.1515/anona-2022-0260","DOIUrl":"https://doi.org/10.1515/anona-2022-0260","url":null,"abstract":"Abstract The article is concerned with systems of fractional discrete equations Δ α x ( n + 1 ) = F n ( n , x ( n ) , x ( n − 1 ) , … , x ( n 0 ) ) , n = n 0 , n 0 + 1 , … , {Delta }^{alpha }xleft(n+1)={F}_{n}left(n,xleft(n),xleft(n-1),ldots ,xleft({n}_{0})),hspace{1em}n={n}_{0},{n}_{0}+1,ldots , where n 0 ∈ Z {n}_{0}in {mathbb{Z}} , n n is an independent variable, Δ α {Delta }^{alpha } is an α alpha -order fractional difference, α ∈ R alpha in {mathbb{R}} , F n : { n } × R n − n 0 + 1 → R s {F}_{n}:left{nright}times {{mathbb{R}}}^{n-{n}_{0}+1}to {{mathbb{R}}}^{s} , s ⩾ 1 sgeqslant 1 is a fixed integer, and x : { n 0 , n 0 + 1 , … } → R s x:left{{n}_{0},{n}_{0}+1,ldots right}to {{mathbb{R}}}^{s} is a dependent (unknown) variable. A retract principle is used to prove the existence of solutions with graphs remaining in a given domain for every n ⩾ n 0 ngeqslant {n}_{0} , which then serves as a basis for further proving the existence of bounded solutions to a linear nonhomogeneous system of discrete equations Δ α x ( n + 1 ) = A ( n ) x ( n ) + δ ( n ) , n = n 0 , n 0 + 1 , … , {Delta }^{alpha }xleft(n+1)=Aleft(n)xleft(n)+delta left(n),hspace{1em}n={n}_{0},{n}_{0}+1,ldots , where A ( n ) Aleft(n) is a square matrix and δ ( n ) delta left(n) is a vector function. Illustrative examples accompany the statements derived, possible generalizations are discussed, and open problems for future research are formulated as well.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":"11 1","pages":"1614 - 1630"},"PeriodicalIF":4.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45448471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 6

Infinitely many non-radial solutions for a Choquard equation 一个Choquard方程的无穷多个非径向解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0224

Fashun Gao, Minbo Yang

引用次数: 5

Multiple nodal solutions of the Kirchhoff-type problem with a cubic term 三次项Kirchhoff型问题的多节点解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0225

Tao Wang, Yanling Yang, Hui Guo

{"title":"Multiple nodal solutions of the Kirchhoff-type problem with a cubic term","authors":"Tao Wang, Yanling Yang, Hui Guo","doi":"10.1515/anona-2022-0225","DOIUrl":"https://doi.org/10.1515/anona-2022-0225","url":null,"abstract":"Abstract In this article, we are interested in the following Kirchhoff-type problem (0.1) − a + b ∫ R N ∣ ∇ u ∣ 2 d x Δ u + V ( ∣ x ∣ ) u = ∣ u ∣ 2 u in R N , u ∈ H 1 ( R N ) , left{begin{array}{l}-left(a+bmathop{displaystyle int }limits_{{{mathbb{R}}}^{N}}| nabla uhspace{-0.25em}{| }^{2}{rm{d}}xright)Delta u+Vleft(| x| )u=| uhspace{-0.25em}{| }^{2}uhspace{1.0em}{rm{in}}hspace{0.33em}{{mathbb{R}}}^{N}, uin {H}^{1}left({{mathbb{R}}}^{N}),end{array}right. where a , b > 0 , N = 2 a,bgt 0,N=2 or 3, the potential function V V is radial and bounded from below by a positive number. Because the nonlocal b ∣ ∇ u ∣ L 2 ( R N ) 2 Δ u b| nabla uhspace{-0.25em}{| }_{{L}^{2}left({{mathbb{R}}}^{N})}^{2}Delta u is 3-homogeneous which is in complicated competition with the nonlinear term ∣ u ∣ 2 u | uhspace{-0.25em}{| }^{2}u . This causes that not all function in H 1 ( R N ) {H}^{1}left({{mathbb{R}}}^{N}) can be projected on the Nehari manifold and thereby the classical Nehari manifold method does not work. By introducing the Gersgorin Disk theorem and the Miranda theorem, via a limit approach and subtle analysis, we prove that for each positive integer k k , equation (0.1) admits a radial nodal solution U k , 4 b {U}_{k,4}^{b} having exactly k k nodes. Moreover, we show that the energy of U k , 4 b {U}_{k,4}^{b} is strictly increasing in k k and for any sequence { b n } left{{b}_{n}right} with b n → 0 + , {b}_{n}to {0}_{+}, up to a subsequence, U k , 4 b n {U}_{k,4}^{{b}_{n}} converges to U k , 4 0 {U}_{k,4}^{0} in H 1 ( R N ) {H}^{1}left({{mathbb{R}}}^{N}) , which is a radial nodal solution with exactly k k nodes of the classical Schrödinger equation − a Δ u + V ( ∣ x ∣ ) u = ∣ u ∣ 2 u in R N , u ∈ H 1 ( R N ) . left{begin{array}{l}-aDelta u+Vleft(| x| )u=| uhspace{-0.25em}{| }^{2}uhspace{1.0em}{rm{in}}hspace{0.33em}{{mathbb{R}}}^{N}, uin {H}^{1}left({{mathbb{R}}}^{N}).end{array}right. Our results extend the existence result from the super-cubic case to the cubic case.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":"11 1","pages":"1030 - 1047"},"PeriodicalIF":4.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48120538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 5

Thresholds for the existence of solutions to inhomogeneous elliptic equations with general exponential nonlinearity 具有一般指数非线性的非齐次椭圆型方程解存在性的阈值

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2021-0220

Kazuhiro Ishige, S. Okabe, Tokushi Sato

引用次数: 2

Nontrivial solutions of discrete Kirchhoff-type problems via Morse theory 基于Morse理论的离散kirchhoff型问题非平凡解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0251

Y. Long

引用次数: 15

The existence and multiplicity of the normalized solutions for fractional Schrödinger equations involving Sobolev critical exponent in the L2-subcritical and L2-supercritical cases 涉及Sobolev临界指数的分数阶Schrödinger方程在l2 -亚临界和l2 -超临界情况下归一化解的存在性和多重性

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0252

Quanqing Li, W. Zou

{"title":"The existence and multiplicity of the normalized solutions for fractional Schrödinger equations involving Sobolev critical exponent in the L2-subcritical and L2-supercritical cases","authors":"Quanqing Li, W. Zou","doi":"10.1515/anona-2022-0252","DOIUrl":"https://doi.org/10.1515/anona-2022-0252","url":null,"abstract":"Abstract This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: (P) ( − Δ ) s u + λ u = μ ∣ u ∣ p − 2 u + ∣ u ∣ 2 s ∗ − 2 u , x ∈ R N , u > 0 , ∫ R N ∣ u ∣ 2 d x = a 2 , left{begin{array}{l}{left(-Delta )}^{s}u+lambda u=mu | u{| }^{p-2}u+| u{| }^{{2}_{s}^{ast }-2}u,hspace{1em}xin {{mathbb{R}}}^{N},hspace{1.0em} ugt 0,hspace{1em}mathop{displaystyle int }limits_{{{mathbb{R}}}^{N}}| u{| }^{2}{rm{d}}x={a}^{2},hspace{1.0em}end{array}right. where 0 < s < 1 0lt slt 1 , a a , μ > 0 mu gt 0 , N ≥ 2 Nge 2 , and 2 < p < 2 s ∗ 2lt plt {2}_{s}^{ast } . We consider the L 2 {L}^{2} -subcritical and L 2 {L}^{2} -supercritical cases. More precisely, in L 2 {L}^{2} -subcritical case, we obtain the multiplicity of the normalized solutions for problem ( P ) left(P) by using the truncation technique, concentration-compactness principle, and genus theory. In L 2 {L}^{2} -supercritical case, we obtain a couple of normalized solution for ( P ) left(P) by using a fiber map and concentration-compactness principle. To some extent, these results can be viewed as an extension of the existing results from Sobolev subcritical growth to Sobolev critical growth.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":"11 1","pages":"1531 - 1551"},"PeriodicalIF":4.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46463248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 13

Infinitely many radial and non-radial sign-changing solutions for Schrödinger equations Schrödinger方程的无穷多径向和非径向变号解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2021-0221

Gui-Dong Li, Yong-Yong Li, Chunlei Tang

引用次数: 2

On the solutions to p-Poisson equation with Robin boundary conditions when p goes to +∞ p趋于+∞时具有Robin边界条件的p- poisson方程的解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0258

Vincenzo Amato, Alba Lia Masiello, C. Nitsch, C. Trombetti

引用次数: 2

Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities 临界非线性非齐次分数(p, q)-拉普拉斯系统的解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0248

Mengfei Tao, Binlin Zhang

引用次数: 5

Global gradient estimates for Dirichlet problems of elliptic operators with a BMO antisymmetric part 具有BMO反对称部分的椭圆算子Dirichlet问题的全局梯度估计

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0247

Sibei Yang, Dachun Yang, Wen Yuan

{"title":"Global gradient estimates for Dirichlet problems of elliptic operators with a BMO antisymmetric part","authors":"Sibei Yang, Dachun Yang, Wen Yuan","doi":"10.1515/anona-2022-0247","DOIUrl":"https://doi.org/10.1515/anona-2022-0247","url":null,"abstract":"Abstract Let n ≥ 2 nge 2 and Ω ⊂ R n Omega subset {{mathbb{R}}}^{n} be a bounded nontangentially accessible domain. In this article, the authors investigate (weighted) global gradient estimates for Dirichlet boundary value problems of second-order elliptic equations of divergence form with an elliptic symmetric part and a BMO antisymmetric part in Ω Omega . More precisely, for any given p ∈ ( 2 , ∞ ) pin left(2,infty ) , the authors prove that a weak reverse Hölder inequality with exponent p p implies the global W 1 , p {W}^{1,p} estimate and the global weighted W 1 , q {W}^{1,q} estimate, with q ∈ [ 2 , p ] qin left[2,p] and some Muckenhoupt weights, of solutions to Dirichlet boundary value problems. As applications, the authors establish some global gradient estimates for solutions to Dirichlet boundary value problems of second-order elliptic equations of divergence form with small BMO {rm{BMO}} symmetric part and small BMO {rm{BMO}} antisymmetric part, respectively, on bounded Lipschitz domains, quasi-convex domains, Reifenberg flat domains, C 1 {C}^{1} domains, or (semi-)convex domains, in weighted Lebesgue spaces. Furthermore, as further applications, the authors obtain the global gradient estimate, respectively, in (weighted) Lorentz spaces, (Lorentz–)Morrey spaces, (Musielak–)Orlicz spaces, and variable Lebesgue spaces. Even on global gradient estimates in Lebesgue spaces, the results obtained in this article improve the known results via weakening the assumption on the coefficient matrix.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":"11 1","pages":"1496 - 1530"},"PeriodicalIF":4.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43249751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 1