Existence of solution for a class of nonvariational Kirchhoff type problem via dynamical methods. (August 2020) - Alves, Claudianor O.; Boudjeriou, Tahir
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.