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.
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页码：98 / 105
页数：8
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