Infinitely many non-radial positive solutions to the double-power nonlinear Schrodinger equations

We consider the following problem with combined nonlinearities: {-Delta u + a(y)u + b(y)u(q) - u(p) = 0, u > 0, in R-N, u is an element of H-1(R-N), where 1 < p < 2* - 1, q > 1, 2* = 2N/N-2 when N >= 3; 2* = +infinity when N = 2. By use of the Lyapunov-Schmidt reduction argument, under some expansion conditions of the potentials a(y) and b(y), we establish infinitely many non-radial solutions. Especially, the nonlinearity b(y)uq is allowed to be (super-)critical, that is, q >= 2* - 1.