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This paper is concerned with the following nonlinear Schrödinger equations with magnetic potentials... (∇/i-αA(∣x∣))2 u + (1 + αV(∣x∣)) u= ∣u∣ p-2u, u ϵH1(RN, C) where 2 < p < 2N /N-2 if N ⩾3 and 2 0(∣ = 1.....,N) is a real C1 bounded function on RN and V (∣x∣)> (j=1...,N) is a real continuous electric potential. Under some decaying conditions of both electric and magnetic potentials which are given in section 1, we prove that the equation has multiple complex-valued solutions by applying the finite reduction method. [ABSTRACT FROM AUTHOR]

In this paper, we study a fractional nonlinear Schrödinger equation. Applying the finite reduction method, we prove that the equation has multi-bump positive solutions under some suitable conditions which are given in section 1. [ABSTRACT FROM AUTHOR]