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.

Keywords

• critical point
• positive solution
• kirchhoff-type problems
• 35j60
• 35j20
• 35k20
• 47j30