Multiplicity results for elliptic Kirchhoff-type problems

Abstract The aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach combines variational methods with properties of nonlocal fractional operators

Existence and multiplicity results for a coupled system of Kirchhoff type equations

This paper deals with a coupled system of Kirchhoff type equations in ${\mathbb{R}}^{3}$. Under suitable assumptions on the potential functions $V(x)$ and $W(x)$, we obtain the existence and multiplicity of nontrivial solutions when the parameter $\lambda$ is sufficiently large. The method combines the Nehari manifold and the mountain-pass theorem