Multiple solutions for the fourth-order elliptic equation with vanishing potential

被引：12

作者：

Zhang, Wen ^{[1
]}

Zhang, Jian ^{[1
]}

Luo, Zhiming ^{[1
]}

机构：

[1] Hunan Univ Commerce, Sch Math & Stat, Changsha 410205, Hunan, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2017年 / 73卷

关键词：

Fourth-order elliptic equation; Mixed nonlinearity; Vanishing potential; Variational methods; NONLINEAR SCHRODINGER-EQUATIONS; EXISTENCE; INFINITY;

D O I：

10.1016/j.aml.2017.04.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the following fourth-order elliptic equation {Delta(2)u-Delta u+V(x)u= k(x)f(u) + mu xi(x)vertical bar u vertical bar(p-2)u, x is an element of R-N, u is an element of H-2 (R-N) where Delta(2) := Delta (Delta) is the biharmonic operator, N >= 5, V, K are nonnegative continuous functions and f is a continuous function with a quasicritical growth. By working in weighted Sobolev spaces and using a variational method, we prove that the above equation has two nontrivial solutions. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：98 / 105

页数：8

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