Existence of solution for a class of nonvariational Kirchhoff type problem via dynamical methods. (August 2020)

• Record Type: Journal Article
• Authors: Alves, Claudianor O.; Boudjeriou, Tahir
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: 35K60 -- 34B10 -- 35J15; Parabolic equations -- Nonlocal problem -- Second-order elliptic equations; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111851
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we use dynamical methods to establish the existence of nontrivial solution for the following class of Kirchhoff type problem ( P ) − 1 + b ∫ Ω | ∇ u | 2 d x Δ u = f ( u ) + h ( u, ∇ u ), x ∈ Ω, u = 0, x ∈ ∂ Ω, where Ω ⊂ R N ( N = 2, 3 ) is a smooth bounded domain, b ≥ 0, f : R → R and h : R × R N → [ 0, + ∞ ) are C 1 -functions that satisfy some technical conditions.