Quasilinear Schrödinger equations with unbounded or decaying potentials

Abstract

AbstractWe study the existence of nonnegative and nonzero solutions for the following class of quasilinear Schrödinger equations: urn:x-wiley:0025584X:media:mana201600028:mana201600028-math-0001where V and Q are potentials that can be singular at the origin, unbounded or vanishing at infinity. In order to prove our existence result we used minimax techniques in a suitable weighted Orlicz space together with regularity arguments and we need to obtain a symmetric criticality type result.