Existence and multiplicity results for supercritical nonlocal Kirchhoff problem
Texas State University, Department of Mathematics
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  where existence and multiplicity results were obtained when g is subcritical and f is a power-type function with critical exponent.
Nonlocal problem, Kirchhoff equation, Weak solution, Supercritical growth, Variational methods
Anello, G. (2023). Existence and multiplicity results for supercritical nonlocal Kirchhoff problem. <i>Electronic Journal of Differential Equations, 2023</i>(14), pp. 1-10.