Fractional $p&q$ Laplacian Problems in RN with Critical Growth

We deal with the following nonlinear problem involving fractional p&q Laplacians: (-Δ)ˢₚu+(-Δ)ˢqu+|u|ᵖ⁻²u+|u|q-2u=λ h(x) f(u)+|u|^{q*ₛ-2}u in RN, where s∈ (0,1) , 1 < p < q < N/s , q^*_s=Nq/N-sq , λ > 0 is a parameter, h is a nontrivial bounded perturbation and f is a superlinear continuous function with subcritical growth. Using suitable variational arguments and concentration-compactness lemma, we prove the existence of a nontrivial non-negative solution for λ sufficiently large.