A POSITIVE SOLUTION FOR AN ASYMPTOTICALLY CUBIC QUASILINEAR SCHRODINGER EQUATION

被引：4

作者：

Fang, Xiang-Dong ^{[1
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2019年 / 18卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Quasilinear Schrodinger equation; positive solution; asymptotically cubic; Nehari manifold; SCALAR FIELD-EQUATIONS; SOLITON-SOLUTIONS; EXISTENCE; STATES; UNIQUENESS;

D O I：

10.3934/cpaa.2019004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following quasilinear Schrodinger equation -Delta u + V(x)u - Delta(u(2))u = q(x)g(u), x is an element of R-N,R- where N >= 1, 0 < q(x) <= lim(vertical bar x vertical bar ->infinity) q(x), g is an element of C (R+, R) and g(u)/u(3)-> 1, as u ->infinity. We establish the existence of a positive solution to this problem by using the method developed in Szulkin and Weth [27, 28].

引用

页码：51 / 64

页数：14

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