A class of p–qp–q-Laplacian type equation with concave–convex nonlinearities in bounded domain

In this paper, our main purpose is to establish the existence of multiple solutions of a class of p–qp–q-Laplacian equation involving concave–convex nonlinearities:{−Δpu−Δqu=θV(x)|u|r−2u+|u|p⁎−2u+λf(x,u),x∈Ω,u=0,x∈∂Ω where Ω   is a bounded domain in RNRN, λ,θ>0λ,θ>0, 10λ⁎>0 is a constant, there is a θ⁎>0θ⁎>0, such that for every θ∈(0,θ⁎)θ∈(0,θ⁎), the above problem possesses infinitely many weak solutions. We also obtain some results for the case 1