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We consider the following problem with combined nonlinearities:wherewhen;when  N  = 2. By use of the Lyapunov-Schmidt reduction argument, under some expansion conditions of the potentialsand, we establish infinitely many non-radial solutions. Especially, the nonlinearityis allowed to be (super-)critical, that is,.

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