FRACTIONAL p&q-LAPLACIAN PROBLEMS WITH POTENTIALS VANISHING AT INFINITY

In this paper we prove the existence of a positive and a negative ground state weak solution for the following class of fractional p&q-Laplacian problems (-Delta)(P)(s)u + (-Delta)(P)(s)u+V(x)(vertical bar u vertical bar(p-2)u +vertical bar i vertical bar(q-2) u) = K(x) f(u) in R-N, where s is an element of(0,1), 1N -> R and K : R-N -> R are continuous, positive functions, allowed for vanishing behavior at infinity, f is a continuous function with quasicritical growth and the leading operator (-Delta)(t)(s), with t is an element of {p, q}, is the fractional t-Laplacian operator.