Electron. J. Differential Equations, Vol. 2023 (2023), No. 14, pp. 1-10.

Existence and multiplicity results for supercritical nonlocal Kirchhoff problem

Giovanni Anello

We study the existence and multiplicity of solutions for the nonlocal perturbed Kirchhoff problem $$\displaylines{-\Big(a+b\int_\Omega |\nabla u|^2\,dx\Big)\Delta u=\lambda g(x,u)+f(x,u), \quad \text{in } \Omega,\\ u=0, \quad\text{on }\partial\Omega,}$$ 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.
DOI: https://doi.org/10.58997/ejde.2023.14

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Giovanni Anello
Department of Mathematics and Computer Science
Physical Science and Earth Science
University of Messina
Viale F. Stagno d'Alcontres 31, Italy
email: ganello@unime.it

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