Multiplicity results for elliptic Kirchhoff-type problems

Sami Baraket, Giovanni Molica Bisci
2017 Advances in Nonlinear Analysis  
AbstractThe 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.
doi:10.1515/anona-2015-0168 fatcat:66ydxpdcjzat5fsgl4lfnd2tfu