On nodal solutions for a class of fourth-order elliptic equations

被引：0

作者：

Benhassine, Abderrazek ^{[1
]}

Farhani, Saida ^{[2
]}

Talbi, Taib ^{[2
]}

机构：

[1] Higher Inst Sci Comp & Math, Monastir, Tunisia

[2] Fac Sci Sfax, Sfax, Tunisia

来源：

JOURNAL OF ANALYSIS | 2025年

关键词：

Fourth-order equations; Nonlinear eigenvalue problem; Nodal solutions; SIGN-CHANGING SOLUTIONS; NONTRIVIAL SOLUTIONS; EXISTENCE; MULTIPLICITY;

D O I：

10.1007/s41478-025-00907-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the equation {Delta(2)u+c Delta u=lambda f(x,u), x is an element of Omega, u=Delta u=0, x is an element of partial derivative Omega, where Delta(2) denotes the biharmonic operator, c is a given constant, Omega is a bounded domain in R-n(n >= 1) with smooth boundary partial derivative Omega, and lambda>0 is a parameter. The nonlinearity f exhibits an oscillatory behavior. We establish the existence of multiple positive solutions, multiple negative solutions, and multiple sign-changing solutions, depending on lambda.

引用

页数：16

共 16 条

[1]

Abrahams ID, 2002, FLUID MEC A, V68, P303

[2] Existence of nontrivial solutions of an asymptotically linear fourth-order elliptic equation [J].