Existence and concentration result for a quasilinear Schrödinger equation with critical growth
Existence and concentration result for a quasilinear Schrödinger equation with critical growth
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DOI：
10.1007/s00033-017-0869-6
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发表时间：
2017-10
期刊：
影响因子：
--
通讯作者：
Liuyang Shao;Haibo Chen
中科院分区：
文献类型：
--
作者：
Liuyang Shao;Haibo Chen
This paper is concerned with the concentration of positive ground states solutions for a modified Schrödinger equation $$\begin{aligned} -\varepsilon ^{2}\triangle u+V(x)u-\varepsilon ^{2}\triangle (u^{2})u=K(x)|u|^{p-2}u+|u|^{22^{*}-2}u,\quad \text{ in } \; \mathbb {R}^{N}, \end{aligned}$$whereis a parameter andis the critical Sobolev exponent. We prove the existence of a positive ground state solutionandsufficiently small under some suitable conditions on the nonnegative functionsV(x) andK(x). Moreover,concentrates around a global minimum point ofVas. The proof of the main result is based on minimax theorems and concentration compact theory.
This paper is concerned with the concentration of positive ground states solutions for a modified Schrödinger equation $$\begin{aligned} -\varepsilon ^{2}\triangle u+V(x)u-\varepsilon ^{2}\triangle (u^{2})u=K(x)|u|^{p-2}u+|u|^{22^{*}-2}u,\quad \text{ in } \; \mathbb {R}^{N}, \end{aligned}$$whereis a parameter andis the critical Sobolev exponent. We prove the existence of a positive ground state solutionandsufficiently small under some suitable conditions on the nonnegative functionsV(x) andK(x). Moreover,concentrates around a global minimum point ofVas. The proof of the main result is based on minimax theorems and concentration compact theory.