Existence and multiplicity results for supercritical nonlocal Kirchhoff problem
Date
2023-02-15
Authors
Anello, Giovanni
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the existence and multiplicity of solutions for the nonlocal perturbed Kirchhoff problem
-(α + b)∫Ω |∇u|2dx) ∆u = λg(x, u) + ƒ(x, u), in Ω,
u = 0, on ∂Ω,
where Ω is a bounded smooth domain in ℝN, N>4, a,b,&lambda>0, and ƒ, g : Ω x ℝ → ℝ are Caratheodory functions, with f subcritical, and g of arbitrary growth. This paper is motivated by a recent results by Faraci and Silva [4] where existence and multiplicity results were obtained when g is subcritical and f is a power-type function with critical exponent.
Description
Keywords
Nonlocal problem, Kirchhoff equation, Weak solution, Supercritical growth, Variational methods
Citation
Anello, G. (2023). Existence and multiplicity results for supercritical nonlocal Kirchhoff problem. <i>Electronic Journal of Differential Equations, 2023</i>(14), pp. 1-10.