Infinitely many high energy solutions for fourth-order ellip- tic equations with p-Laplacian in bounded domain

被引：3

作者：

Chahma, Youssouf ^{[1
,2
]}

Chen, Haibo ^{[1
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Univ Sci & Technol Houari Boumediene, Fac Math, PB 32, Bab Ezzouar 16111, Algiers, Algeria

来源：

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS | 2024年 / 32卷 / 02期

关键词：

Variational methods; p-Laplacian; fourth-order elliptic equations; SIGN-CHANGING SOLUTIONS; BIHARMONIC-EQUATIONS; NONTRIVIAL SOLUTIONS; SCHRODINGER-EQUATIONS; MULTIPLICITY; EXISTENCE;

D O I：

10.22436/jmcs.032.02.02

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the following fourth-order elliptic equation with p-Laplacian, steep potential well and sublinear perturbation: { & UDelta;2u-& kappa;& UDelta;pu+ & mu;V(x)u = f(x, u) + & xi;(x)|u|q-2u, x E & omega;, u = & UDelta;u = 0, on partial differential & omega;, where N ? 5, & omega; is a bounded domain in RN with smooth boundary partial differential & omega;, & UDelta;2:= & UDelta;(& UDelta;) is the biharmonic operator, & UDelta;pu div (|Vu|p-2Vu)with p > 2, & mu;, & kappa; > 0 are parameters, f E C (& omega; x R,R), & xi; E L 2 2-q (& omega;) with 1 q < 2, we have the potential V E C(& omega;,R). Using variational methods, we establish the existence of infinitely many nontrivial high energy solutions under certain assumptions on V and f.

引用

页码：109 / 121

页数：13

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