Existence of Solutions for a Quasilinear Schrodinger Equation with Potential Vanishing

被引：0
|
作者：
Xue, Yan-fang [1 ]
Han, Jian-xin [1 ]
Zhu, Xin-cai [1 ]
机构：
[1] Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Henan, Peoples R China
来源：
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2023年 / 39卷 / 03期
基金：
中国国家自然科学基金;
关键词：
quasilinear Schrodinger equation; vanishing potential; asymptotically cubic; mountain pass theorem; SOLITON-SOLUTIONS;
D O I：
10.1007/s10255-023-1083-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the following quasilinear Schrodinger equation -Delta u + V(x)u-Delta(u(2))u = K(x)g(u); x epsilon R-3; where the nonlinearity g (u) is asymptotically cubic at infinity, the potential V (x) may vanish at infinity. Under appropriate assumptions on K(x), we establish the existence of a nontrivial solution by using the mountain pass theorem.
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页码：696 / 706
页数：11
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