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Quasilinear Schrödinger equations with unbounded or decaying potentials

Author

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  • Uberlandio B. Severo
  • Gilson M. de Carvalho

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.

Suggested Citation

  • Uberlandio B. Severo & Gilson M. de Carvalho, 2018. "Quasilinear Schrödinger equations with unbounded or decaying potentials," Mathematische Nachrichten, Wiley Blackwell, vol. 291(2-3), pages 492-517, February.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:2-3:p:492-517
    DOI: 10.1002/mana.201600028
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    Cited by:

    1. Ohsang Kwon, 2020. "Nonexistence of Positive Solutions for Quasilinear Equations with Decaying Potentials," Mathematics, MDPI, vol. 8(3), pages 1-7, March.

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