On existence of two nontrivial solutions to Dirichlet problem involving non- local fractional p-Laplace

Abstract

The aim of this paper is to study the existence solutions for Dirichlet problem involving nonlocal p-fractional Laplacian ...

where is a parameter, Lp K is a non-local operator with singular kernel K; is
an open bounded subset of RN with Lipschitz boundary @ ; f is a Carath²odory
function. By using Morse theory, we get the existence two solutions of above
problem. In our best knowledge, this result is new.