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 (−∆)pu + (−∆)qu + V (x)(|u|p−2u + |u|q−2u) = K(x)f(u) in R , where s ∈ (0, 1), 1 < p < q < N s , V : R→R and K : R→R are continuous, positive functions, allowed for vanishing behavior at infinity, f is a continuous function with quasicritical growth and the leading operator (−∆)t , with t ∈ {p, q}, is the fractional t-Laplacian operator.