Let p > q and let G be the group U(p, q) or Spin0(p, q). Let P = LN be the maximal parabolic subgroup of G with Levi subgroup L ∼=M × U where (M,U) = { (GLq(C),U(p− q)) if G = U(p, q) (GLq (R),Spin(p− q)) if G = Spin0(p, q). Let χ be a 1 dimensional character of M and τ an irreducible representation of U with highest weight μ. Let πχ,μ be the representation of P which is trivial on N and πχ,μ|L...

In this paper, we study the nonlocal equation ∫RN|u(x)|2dxγΔu=λu+μ|u|q−2u+|u|p−2u, xinRN having a prescribed mass ∫RN|u(x)|2dx=c2, where N≥3, μ, γ∈(0,+∞), q∈(2,2∗), c is positive constant, p, q∈(2,2∗) with p≠q and 2∗=2NN−2. This research meaningful from physical point of view. Using variational methods, present some results on nonexistence existence solutions under different cases p q which imp...