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

页码：573 / 583

页数：11

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