Existence and multiplicity results for supercritical nonlocal Kirchhoff problem
DOI:
https://doi.org/10.58997/ejde.2023.14Abstract
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.
For more information see https://ejde.math.txstate.edu/Volumes/2023/14/abstr.html
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