Multiple solutions to boundary value problems for semilinear elliptic equations

Electronic Journal of Differential Equations

article

Duong Trong Luyen¹  Nguyen Minh Tri² 

[1] Division of Computational Mathematics and Engineering Institute for Computational Science, and Faculty of Mathematics and Statistics Ton Duc Thang University;Institute of Mathematics Vietnam Academy of Science and Technology 18 Hoang Quoc Viet 10307 Cau Giay

关键词: Semilinear elliptic equations;    multiple solutions;    critical points;    perturbation methods;    boundary value problem.;   

DOI  :  10.58997/ejde.2021.48

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

In this article, we study the multiplicity of weaksolutions to the boundary value problemwhere Ω is a bounded domain with smooth boundary in RN 2),f(x,ξ) is odd in ξ and g is a perturbation term.Under some growth conditions on f and g, we show that there are infinitely manysolutions. Here we do not require that f be continuous or satisfy theAmbrosetti-Rabinowitz (AR) condition.The conditions assumed here are not implied by the ones in [3,15].We use the perturbation method by Rabinowitz combined with estimating theasymptotic behavior of eigenvalues for Schrödinger's equations.

【 授权许可】

CC BY