The effect of the domain topology on the number of positive solutions of an elliptic Kirchhoff problem. (April 2016)

• Record Type: Journal Article
• Authors: Santos Junior, João R.
• Is Part Of: Nonlinear analysis. Volume 28(2016)
• Page Start: 269
• Page End: 283
• Publication Date: 2016-04
• Subjects: Schrödinger–Kirchhoff type problem -- Lusternik–Schnirelmann theory -- Expanding domain; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.10.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Using minimax methods and Lusternik–Schnirelmann theory, we study multiple positive solutions for the Schrödinger–Kirchhoff equation M ( ∫ Ω λ | ∇ u | 2 d x + ∫ Ω λ u 2 d x ) [ − Δ u + u ] = f ( u ) in Ω λ = λ Ω . The set Ω ⊂ R 3 is a smooth bounded domain, λ > 0 is a parameter, M is a general continuous function and f is a superlinear continuous function with subcritical growth. Our main result relates, for large values of λ, the number of solutions with the least number of closed and contractible in Ω ¯ which cover Ω ¯ .