Abstract
In this paper, we are concerned with a nonlinear Schrödinger equation whose nonlinear term contains a positive parameter λ and has a superlinear growth only locally. Moreover, we are interested in the situation where the potential V(x) is invariant under a finite group action G, which enables us to treat the case that V(x) is of non-trapping type. By considering several auxiliary problems, we are able to obtain the existence of a G-invariant positive solution when the parameter λ is sufficiently large.
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