Multiple positive solutions for a p-Laplace Benci-Cerami type problem (1 < p < 2), via Morse theory

被引：0

作者：

Vannella, Giuseppina ^{[1
]}

机构：

[1] Politecn Bari, Dipartimento Meccan Matemat & Management, Via Orabona 4, I-70125 Bari, Italy

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2023年 / 25卷 / 02期

关键词：

p-Laplace equations; perturbation results; Morse theory; critical groups; NONTRIVIAL SOLUTIONS; ELLIPTIC PROBLEMS; EQUATIONS; EXISTENCE; FUNCTIONALS;

D O I：

10.1142/S0219199721500656

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let us consider the quasilinear problem(P-epsilon) {-epsilon(p) Delta(p)u + u(p-1) = f(u) in Omega,u > 0 in Omega,u = 0 on theta Omega,where Omega is a bounded domain in R-N with smooth boundary, N >= 2, 1 < p < 2, epsilon > 0 is a parameter and f : R -> R is a continuous function with f(0) = 0, having a subcritical growth. We prove that there exists epsilon(*) > 0 such that, for every epsilon is an element of (0, epsilon(*)), (P-epsilon) has at least 2P(1)(Omega) -1 solutions, possibly counted with their multiplicities, where P-t(Omega) is the Poincare polynomial of Omega. Using Morse techniques, we furnish an interpretation of the multiplicity of a solution, in terms of positive distinct solutions of a quasilinear equation on Omega, approximating (P-epsilon).

引用

页数：20

共 49 条

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Multiple positive solutions for a p-Laplace Benci-Cerami type problem (1 &lt; p &lt; 2), via Morse theory

Multiple positive solutions for a p-Laplace Benci-Cerami type problem (1 < p < 2), via Morse theory