Multiplicity of positive solutions for a fractional p&q-Laplacian problem in [formula omitted

Abstract

In this paper we deal with the following fractional p&q-Laplacian problem:{(−Δ)psu+(−Δ)qsu+V(εx)(|u|p−2u+|u|q−2u)=f(u) in RN,u∈Ws,p(RN)∩Ws,q(RN),u>0 in RN, where s∈(0,1), ε>0 is a small parameter, 2≤p<q<Ns, (−Δ)ts, with t∈{p,q}, is the fractional (s,t)-Laplacian operator, V:RN→R is a continuous function satisfying the global Rabinowitz condition, and f:R→R is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik-Schnirelmann category theory, we prove that the above problem admits multiple solutions for ε>0 small enough.