Abstract
Abstract In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving subcritical growth at resonance. By using a change of variables, the quasilinear equation is reduced to a semilinear one, whose associated functional is well defined in the usual Sobolev space. The “first” eigenvalue type of a nonhomogeneous operator has been studied. Using this fact and a variant of the monotone operator theorem, we show that the problem at resonance has at least one nontrivial solution.
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