Electron. J. Differential Equations, Vol. 2023 (2023), No. 14, pp. 110.
Existence and multiplicity results for supercritical nonlocal Kirchhoff problem
Giovanni Anello
Abstract:
We study the existence and multiplicity of solutions for the nonlocal
perturbed Kirchhoff problem
$$\displaylines{\Big(a+b\int_\Omega \nabla u^2\,dx\Big)\Delta u=\lambda g(x,u)+f(x,u), \quad \text{in } \Omega,\\ u=0, \quad\text{on }\partial\Omega,}$$
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 powertype 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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