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Advances in Nonlinear Analysis最新文献

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Editorial to Special issue “Nonlinear analysis: Perspectives and synergies” 《非线性分析：前景与协同作用》特刊编辑
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0302
Vicentiu D. Rădulescu, Runzhang Xu
{"title":"Editorial to Special issue “Nonlinear analysis: Perspectives and synergies”","authors":"Vicentiu D. Rădulescu, Runzhang Xu","doi":"10.1515/anona-2022-0302","DOIUrl":"https://doi.org/10.1515/anona-2022-0302","url":null,"abstract":"","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47717068","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: 0
Groundstate for the Schrödinger-Poisson-Slater equation involving the Coulomb-Sobolev critical exponent 库仑-索博列夫临界指数Schrödinger-Poisson-Slater方程的基态
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0299
Chun-Yu Lei, Jun Lei, H. Suo
{"title":"Groundstate for the Schrödinger-Poisson-Slater equation involving the Coulomb-Sobolev critical exponent","authors":"Chun-Yu Lei, Jun Lei, H. Suo","doi":"10.1515/anona-2022-0299","DOIUrl":"https://doi.org/10.1515/anona-2022-0299","url":null,"abstract":"Abstract In this article, we study the existence of ground state solutions for the Schrödinger-Poisson-Slater type equation with the Coulomb-Sobolev critical growth: − Δ u + 1 4 π ∣ x ∣ ∗ ∣ u ∣ 2 u = ∣ u ∣ u + μ ∣ u ∣ p − 2 u , in R 3 , -Delta u+left(frac{1}{4pi | x| }ast | u{| }^{2}right)u=| u| u+mu | u{| }^{p-2}u,hspace{1.0em}{rm{in}}hspace{0.33em}{{mathbb{R}}}^{3}, where μ > 0 mu gt 0 and 3 < p < 6 3lt plt 6 . With the help of the Nehari-Pohozaev method, we obtain a ground-state solution for the above equation by employing compactness arguments.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45264599","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: 0
Existence of solutions for a double-phase variable exponent equation without the Ambrosetti-Rabinowitz condition 不含Ambrosetti-Rabinowitz条件的双相变指数方程解的存在性
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0292
Jingjing Liu, P. Pucci
{"title":"Existence of solutions for a double-phase variable exponent equation without the Ambrosetti-Rabinowitz condition","authors":"Jingjing Liu, P. Pucci","doi":"10.1515/anona-2022-0292","DOIUrl":"https://doi.org/10.1515/anona-2022-0292","url":null,"abstract":"Abstract The article deals with the existence of a pair of nontrivial nonnegative and nonpositive solutions for a nonlinear weighted quasilinear equation in R N {{mathbb{R}}}^{N} , which involves a double-phase general variable exponent elliptic operator A {bf{A}} . More precisely, A {bf{A}} has behaviors like ∣ ξ ∣ q ( x ) − 2 ξ {| xi | }^{qleft(x)-2}xi if ∣ ξ ∣ | xi | is small and like ∣ ξ ∣ p ( x ) − 2 ξ {| xi | }^{pleft(x)-2}xi if ∣ ξ ∣ | xi | is large. Existence is proved by the Cerami condition instead of the classical Palais-Smale condition, so that the nonlinear term f ( x , u ) fleft(x,u) does not necessarily have to satisfy the Ambrosetti-Rabinowitz condition.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44334825","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: 4
Nodal solutions with a prescribed number of nodes for the Kirchhoff-type problem with an asymptotically cubic term 具有渐近三次项的kirchhoff型问题具有规定节点数的节点解
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0323
Tao Wang, Yanling Yang, Hui Guo
{"title":"Nodal solutions with a prescribed number of nodes for the Kirchhoff-type problem with an asymptotically cubic term","authors":"Tao Wang, Yanling Yang, Hui Guo","doi":"10.1515/anona-2022-0323","DOIUrl":"https://doi.org/10.1515/anona-2022-0323","url":null,"abstract":"Abstract In this article, we study the following Kirchhoff equation: (0.1) − ( a + b ‖ ∇ u ‖ L 2 ( R 3 ) 2 ) Δ u + V ( ∣ x ∣ ) u = f ( u ) in R 3 , -(a+bVert nabla u{Vert }_{{L}^{2}left({{mathbb{R}}}^{3})}^{2})Delta u+Vleft(| x| )u=fleft(u)hspace{1.0em}hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{{mathbb{R}}}^{3}, where a , b > 0 a,bgt 0 , V V is a positive radial potential function, and f ( u ) fleft(u) is an asymptotically cubic term. The nonlocal term b ‖ ∇ u ‖ L 2 ( R 3 ) 2 Δ u bVert nabla u{Vert }_{{L}^{2}left({{mathbb{R}}}^{3})}^{2}Delta u is 3-homogeneous in the sense that b ‖ ∇ t u ‖ L 2 ( R 3 ) 2 Δ ( t u ) = t 3 b ‖ ∇ u ‖ L 2 ( R 3 ) 2 Δ u bVert nabla tu{Vert }_{{L}^{2}left({{mathbb{R}}}^{3})}^{2}Delta left(tu)={t}^{3}bVert nabla u{Vert }_{{L}^{2}left({{mathbb{R}}}^{3})}^{2}Delta u , so it competes complicatedly with the asymptotically cubic term f ( u ) fleft(u) , which is totally different from the super-cubic case. By using the Miranda theorem and classifying the domain partitions, via the gluing method and variational method, we prove that for each positive integer k k , equation (0.1) has a radial nodal solution U k , 4 b {U}_{k,4}^{b} , which has exactly k + 1 k+1 nodal domains. 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 } → 0 + , left{{b}_{n}right}to {0}_{+}, up to a subsequence, U k , 4 b n {U}_{k,4}^{{b}_{n}} converges strongly to U k , 4 0 {U}_{k,4}^{0} in H 1 ( R 3 ) {H}^{1}left({{mathbb{R}}}^{3}) , where U k , 4 0 {U}_{k,4}^{0} also has k + 1 k+1 nodal domains exactly and solves the classical Schrödinger equation: − a Δ u + V ( ∣ x ∣ ) u = f ( u ) in R 3 . -aDelta u+Vleft(| x| )u=fleft(u)hspace{1.0em}hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{{mathbb{R}}}^{3}. Our results extend the ones in Deng et al. from the super-cubic case to the asymptotically cubic case.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41354486","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: 0
Modeling Wolbachia infection frequency in mosquito populations via a continuous periodic switching model 通过连续周期切换模型模拟蚊子种群沃尔巴克氏体感染频率
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0297
Yantao Shi, Bo Zheng
{"title":"Modeling Wolbachia infection frequency in mosquito populations via a continuous periodic switching model","authors":"Yantao Shi, Bo Zheng","doi":"10.1515/anona-2022-0297","DOIUrl":"https://doi.org/10.1515/anona-2022-0297","url":null,"abstract":"Abstract In this article, we develop a continuous periodic switching model depicting Wolbachia infection frequency dynamics in mosquito populations by releasing Wolbachia-infected mosquitoes, which is different from the discrete modeling efforts in the literature. We obtain sufficient conditions on the existence of a unique and exactly two periodic solutions and analyze the stability of each periodic solution, respectively. We also provide a brief discussion and several numerical examples to illustrate our theoretical results.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45611647","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: 2
Infinitely many localized semiclassical states for nonlinear Kirchhoff-type equation 非线性kirchhoff型方程的无穷多局域半经典态
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0296
Binhua Feng, Da-Bin Wang, Zhi-Guo Wu
{"title":"Infinitely many localized semiclassical states for nonlinear Kirchhoff-type equation","authors":"Binhua Feng, Da-Bin Wang, Zhi-Guo Wu","doi":"10.1515/anona-2022-0296","DOIUrl":"https://doi.org/10.1515/anona-2022-0296","url":null,"abstract":"Abstract We deal with localized semiclassical states for singularly perturbed Kirchhoff-type equation as follows: − ε 2 a + ε b ∫ R 3 ∣ ∇ v ∣ 2 d x Δ v + V ( x ) v = P ( x ) f ( v ) , x ∈ R 3 , -left({varepsilon }^{2}a+varepsilon bmathop{int }limits_{{{mathbb{R}}}^{3}}| nabla v{| }^{2}{rm{d}}xright)Delta v+Vleft(x)v=Pleft(x)fleft(v),hspace{1em}xin {{mathbb{R}}}^{3}, where V , P ∈ C 1 ( R 3 , R ) V,Pin {C}^{1}left({{mathbb{R}}}^{3},{mathbb{R}}) and bounded away from zero. By applying the penalization approach together with the Nehari manifold approach in the studies of Szulkin and Weth, we obtain the existence of an infinite sequence of localized solutions of higher topological type. In addition, we also give a concrete set as the concentration position of these localized solutions. It is noted that, in our main results, f f only belongs to C ( R , R ) Cleft({mathbb{R}},{mathbb{R}}) and does not satisfy the Ambrosetti-Rabinowitz-type condition.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41607425","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
Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent 具有临界指数的p-Dirichlet到-Neumann算子的非线性椭圆-抛物问题
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0306
Yanhua Deng, Zhong Tan, M. Xie
{"title":"Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent","authors":"Yanhua Deng, Zhong Tan, M. Xie","doi":"10.1515/anona-2022-0306","DOIUrl":"https://doi.org/10.1515/anona-2022-0306","url":null,"abstract":"Abstract We consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent. We first obtain the existence and asymptotic estimates of the global solution, and the sufficient conditions of finite time blowup of the solution by using the energy method. Second, we improve the regularity of solution by Moser-type iteration. Finally, we analyze the long-time asymptotic behavior of the global solution. Moreover, with the help of the concentration compactness principle, we present a precise description of the concentration phenomenon of the solution in the forward time infinity.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43509178","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: 0
Multiple nontrivial solutions of superlinear fractional Laplace equations without (AR) condition 无AR条件的超线性分数阶拉普拉斯方程的多个非平凡解
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0281
Leiga Zhao, Hongrui Cai, Yutong Chen
{"title":"Multiple nontrivial solutions of superlinear fractional Laplace equations without (AR) condition","authors":"Leiga Zhao, Hongrui Cai, Yutong Chen","doi":"10.1515/anona-2022-0281","DOIUrl":"https://doi.org/10.1515/anona-2022-0281","url":null,"abstract":"Abstract In this article, we study a class of nonlinear fractional Laplace problems with a parameter and superlinear nonlinearity ( − Δ ) s u = λ u + f ( x , u ) , in Ω , u = 0 , in R N Ω . left{phantom{rule[-1.25em]{}{0ex}}begin{array}{ll}{left(-Delta )}^{s}u=lambda u+fleft(x,u),hspace{1.0em}& hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}Omega , u=0,hspace{1.0em}& hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{{mathbb{R}}}^{N}backslash Omega right.end{array}right. Multiplicity of nontrivial solutions is obtained when the parameter is near the eigenvalue of the fractional Laplace operator without Ambrosetti and Rabinowitz condition for the nonlinearity. Our methods are the combination of minimax method, bifurcation theory, and Morse theory.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43801670","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: 0
Existence of nontrivial solutions for the Klein-Gordon-Maxwell system with Berestycki-Lions conditions Berestycki-Lions条件下Klein-Gordon-Maxwell系统非平凡解的存在性
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0294
Xiao-Qi Liu, Gui-Dong Li, Chunquan Tang
{"title":"Existence of nontrivial solutions for the Klein-Gordon-Maxwell system with Berestycki-Lions conditions","authors":"Xiao-Qi Liu, Gui-Dong Li, Chunquan Tang","doi":"10.1515/anona-2022-0294","DOIUrl":"https://doi.org/10.1515/anona-2022-0294","url":null,"abstract":"Abstract In this article, we study the following Klein-Gordon-Maxwell system: − Δ u − ( 2 ω + ϕ ) ϕ u = g ( u ) , in R 3 , Δ ϕ = ( ω + ϕ ) u 2 , in R 3 , left{phantom{rule[-1.25em]{}{0ex}}begin{array}{l}-Delta u-left(2omega +phi )phi u=gleft(u),hspace{1.0em}{rm{in}}hspace{1em}{{mathbb{R}}}^{3},hspace{1.0em} Delta phi =left(omega +phi ){u}^{2},hspace{1.0em}{rm{in}}hspace{1em}{{mathbb{R}}}^{3},hspace{1.0em}end{array}right. where ω omega is a constant that stands for the phase; u u and ϕ phi are unknowns and g g satisfies the Berestycki-Lions condition [Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983), 313–345; Nonlinear scalar field equations. II. Existence of infinitelymany solutions, Arch. Rational Mech. Anal. 82 (1983), 347–375]. The Klein-Gordon-Maxwell system is a model describing solitary waves for the nonlinear Klein-Gordon equation interacting with an electromagnetic field. By using variational methods and some analysis techniques, the existence of positive solution and multiple solutions can be obtained. Moreover, we study the properties of decay estimates and asymptotic behavior for the positive solution.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49360375","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: 0
Global Sobolev regular solution for Boussinesq system Boussinesq系统的全局Sobolev正则解
IF 4.2 1区 数学
Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0298
Xiaofeng Zhao, Weijia Li, Weiping Yan
{"title":"Global Sobolev regular solution for Boussinesq system","authors":"Xiaofeng Zhao, Weijia Li, Weiping Yan","doi":"10.1515/anona-2022-0298","DOIUrl":"https://doi.org/10.1515/anona-2022-0298","url":null,"abstract":"Abstract This article is concerned with the study of the initial value problem for the three-dimensional viscous Boussinesq system in the thin domain Ω ≔ R 2 × ( 0 , R ) Omega := {{mathbb{R}}}^{2}times left(0,R) . We construct a global finite energy Sobolev regularity solution ( v , ρ ) ∈ H s ( Ω ) × H s ( Ω ) left({bf{v}},rho )in {H}^{s}left(Omega )times {{mathbb{H}}}^{s}left(Omega ) with the small initial data in the Sobolev space H s + 2 ( Ω ) × H s + 2 ( Ω ) {H}^{s+2}left(Omega )times {{mathbb{H}}}^{s+2}left(Omega ) . Some features of this article are the following: (i) we do not require the initial data to be axisymmetric; (ii) the Sobolev exponent s s can be an arbitrary big positive integer; and (iii) the explicit asymptotic expansion formulas of Sobolev regular solution is given. The key point of the proof depends on the structure of the perturbation system by means of a suitable initial approximation function of the Nash-Moser iteration scheme.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44085152","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
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