文章基本信息

标题：Infinitely many solutions of degenerate quasilinear Schrödinger equation with general potentials
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作者：Yan Meng ; Xianjiu Huang ; Jianhua Chen 等
期刊名称：Boundary Value Problems
印刷版ISSN：1687-2762
电子版ISSN：1687-2770
出版年度：2021
卷号：2021
期号：1
页码：1
DOI：10.1186/s13661-021-01520-x
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the following quasilinear Schrödinger equation: $$ -\operatorname{div}\bigl(a(x,\nabla u)\bigr) V(x) \vert x \vert ^{-\alpha p^{*}} \vert u \vert ^{p-2}u=K(x) \vert x \vert ^{- \alpha p^{*}}f(x,u) \quad \text{in } \mathbb{R}^{N}, $$ where $N\geq 3$ , $1< p< N$ , $-\infty <\alpha <\frac{N-p}{p}$ , $\alpha \leq e\leq \alpha 1$ , $d=1 \alpha -e$ , $p^{*}:=p^{*}(\alpha ,e)=\frac{Np}{N-dp}$ (critical Hardy–Sobolev exponent), V and K are nonnegative potentials, the function a satisfies suitable assumptions, and f is superlinear, which is weaker than the Ambrosetti–Rabinowitz-type condition. By using variational methods we obtain that the quasilinear Schrödinger equation has infinitely many nontrivial solutions.
关键词：35J60 ; 35J20