Multiple solutions for a class of nonhomogeneous fourth-order quasilinear equations with nonlinearities

被引：0
|
作者：
Almuaalemi, Belal [1 ]
Chen, Haibo [1 ]
Khoutir, Sofiane [1 ]
机构：
[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
来源：
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2022年 / 30卷 / 03期
关键词：
Fourth-order quasilinear equations; Multiple solutions; Ekeland's variational principle; Mountain pass theorem; SEMILINEAR SCHRODINGER-EQUATIONS; NONTRIVIAL SOLUTIONS; ELLIPTIC-EQUATIONS; BIHARMONIC-EQUATIONS; CRITICAL EXPONENT; EXISTENCE;
D O I：
10.1007/s12591-018-0421-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we concern with the following nonhomogeneous fourth-order quasilinear equations of the form Delta(2)u - Delta u + V(x)u - k/2 Delta(u)(2)u = f(x, u) + h(x), x is an element of R-N, where Delta(2) := Delta (Delta) is the biharmonic operator, k >= 0, N <= 6, V is an element of C(R-N, R), f is an element of C(R-N x R, R) and h(x) is an element of L-2 (R-N). Under some relaxed assumptions on the nonlinear term f, a new result of multiple nontrivial solutions is obtained via the Ekeland's variational principle and the mountain pass theorem.
引用
收藏
页码：573 / 583
页数：11
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