Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 14, pp. 1-10.

Title: Existence and multiplicity results for supercritical nonlocal Kirchhoff problem
       
Authors: Giovanni Anello (Univ. of Messina, Italy)
         
Abstract:
We study the existence and multiplicity of solutions for the nonlocal
perturbed Kirchhoff problem
$$\displaylines{
-\Big(a+b\int_\Omega |\nabla u|^2\,dx\Big)\Delta u=\lambda g(x,u)+f(x,u), \quad
 \text{in } \Omega,\cr
u=0, \quad\text{on }\partial\Omega,
}$$
where Ω is a bounded smooth domain in $\mathbb{R}^N$, N>4, a,b,&lambda>0,
and $f,g:\Omega\times \mathbb{R}\to \mathbb{R}$ 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.

Submitted March 20, 2022. Published February 15, 2023.
Math Subject Classifications: 35J20, 35J25.
Key Words: Nonlocal problem; Kirchhoff equation; weak solution; 
           supercritical growth;  variational methods.