EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS

doi:10.1016/S0252-9602(17)30113-3

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (6): 1870-1880.doi: 10.1016/S0252-9602(17)30113-3

• 论文 • 上一篇

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS

李全清¹, 吴鲜²

1. Department of Mathematics, Honghe University, Mengzi 661100, China;
2. Department of Mathematics, Yunnan Normal University, Kunming 650092, China

收稿日期:2016-02-29 修回日期:2017-04-29 出版日期:2017-12-25 发布日期:2017-12-25
通讯作者: Xian WU E-mail:wuxian2042@163.com
作者简介:Quanqing LI,shili06171987@126.com
基金资助:
This work was supported in part by the National Natural Science Foundation of China (11501403; 11461023) and the Shanxi Province Science Foundation for Youths under grant 2013021001-3.

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS

Quanqing LI¹, Xian WU²

1. Department of Mathematics, Honghe University, Mengzi 661100, China;
2. Department of Mathematics, Yunnan Normal University, Kunming 650092, China

Received:2016-02-29 Revised:2017-04-29 Online:2017-12-25 Published:2017-12-25
Contact: Xian WU E-mail:wuxian2042@163.com
Supported by:
This work was supported in part by the National Natural Science Foundation of China (11501403; 11461023) and the Shanxi Province Science Foundation for Youths under grant 2013021001-3.

摘要/Abstract

摘要：

In this paper, we study the following generalized quasilinear Schrödinger equations with critical or supercritical growths
-div(g²(u)∇u) + g(u)g'(u)|∇u|2 + V (x)u=f(x, u) + λ|u|^p-2u, x ∈ R^N,
where λ > 0, N ≥ 3, g:R → R⁺ is a C¹ even function, g(0)=1, g'(s) ≥ 0 for all s ≥ 0,???20170623???((g(s))/(|s|^α-1)):=β > 0 for some α ≥ 1 and (α-1)g(s) > g'(s)s for all s > 0 and p ≥ α2^*. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 using a change of variables and variational method.

关键词: quasilinear Schrödinger equations, critical or supercritical growths, variational methods

Abstract:

Key words: quasilinear Schrödinger equations, critical or supercritical growths, variational methods

李全清, 吴鲜. EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS[J]. 数学物理学报(英文版), 2017, 37(6): 1870-1880.

Quanqing LI, Xian WU. EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS[J]. Acta mathematica scientia,Series B, 2017, 37(6): 1870-1880.

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EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS

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