EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS

被引：0

作者：

李全清 ^{[1
]}

吴鲜 ^{[2
]}

机构：

[1] Department of Mathematics,Honghe University

[2] Department of Mathematics,Yunnan Normal University

来源：

Acta Mathematica Scientia | 2017年 / 37卷 / 06期

基金：

山西省青年科学基金; 中国国家自然科学基金;

关键词：

quasilinear Schrdinger equations; critical or supercritical growths; variational methods;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper,we study the following generalized quasilinear Schrdinger equations with critical or supercritical growths-div(g~2(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 C~1 even function,g(0) = 1,g′(s) ≥ 0 for all s ≥ 0,lim|s|→+∞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 smallλ > 0 using a change of variables and variational method.

引用

页码：1870 / 1880

页数：11

共 50 条

[41] Existence and concentration of positive solutions for a Schrödinger logarithmic equation [J].

Claudianor O. Alves ;

Daniel C. de Morais Filho .

Zeitschrift für angewandte Mathematik und Physik, 2018, 69

[42] Solutions of a quasilinear Schrödinger-Poisson system with linearly bounded nonlinearities [J].

Li, Anran ;

Wei, Chongqing ;

Zhao, Leiga .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (02)

[43] A class of Schrödinger elliptic equations involving supercritical exponential growth [J].

Yony Raúl Santaria Leuyacc .

Boundary Value Problems, 2023

[44] On existence and concentration behavior of positive ground state solutions for a class of fractional Schrödinger–Choquard equations [J].

Zu Gao ;

Xianhua Tang ;

Sitong Chen .

Zeitschrift für angewandte Mathematik und Physik, 2018, 69

[45] Sign-changing solutions to Schrödinger-Kirchhoff-type equations with critical exponent [J].

Liping Xu ;

Haibo Chen .

Advances in Difference Equations, 2016

[46] Existence and asymptotic behaviour of solutions for a quasi-linear Schrödinger–Poisson system with a critical nonlinearity [J].

Giovany M. Figueiredo ;

Gaetano Siciliano .

Zeitschrift für angewandte Mathematik und Physik, 2020, 71

[47] EXISTENCE AND NONEXISTENCE OF NONTRIVIAL SOLUTIONS FOR CHOQUARD TYPE EQUATIONS [J].

Wang, Tao .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,

[48] Multiple solutions of discrete Schrödinger equations with growing potentials [J].

Liqian Jia ;

Guanwei Chen .

Advances in Difference Equations, 2016

[49] Existence of nontrivial solution for quasilinear equations involving the 1-biharmonic operator [J].

Tao, Huo ;

Li, Lin ;

Yang, Xiao-Qiong .

ASYMPTOTIC ANALYSIS, 2023, 133 (04) :535-553

[50] The nontrivial solutions for fractional Schrodinger-Poisson equations with magnetic fields and critical or supercritical growth [J].

Liu, Lintao ;

Chen, Haibo .

APPLIED MATHEMATICS LETTERS, 2021, 121 (121)

← 1 2 3 4 5 →