Quasilinear Schrödinger equations with unbounded or decaying potentials

Uberlandio B. Severo and Gilson M. de Carvalho

Mathematische Nachrichten, 2018, vol. 291, issue 2-3, 492-517

Abstract: We study the existence of nonnegative and nonzero solutions for the following class of quasilinear Schrödinger equations: −Δu+V(|x|)u−[Δ(u2)]u=Q(|x|)g(u),x∈RN,u(x)→0 as |x|→∞,where 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.

Date: 2018
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