Nonlinear elliptic equations in dimension two with potentials which can vanish at infinity

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Abstract

We will focus on the existence of nontrivial solutions to the following nonlinear elliptic equation -Δu + V (x)u = f (u), x ∈ R2, where V is a nonnegative function which can vanish at infinity or be unbounded from above, and f have exponential growth range. The proof involves a truncation argument combined with Mountain Pass Theorem and a Trudinger-Moser type inequality.

Original languageEnglish
Pages (from-to)325-351
Number of pages27
JournalProyecciones
Volume38
Issue number2
DOIs
StatePublished - Jun 2019

Bibliographical note

Publisher Copyright:
© 2019, Proyecciones Journal of Mathematics.

Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

Keywords

  • Nonlinear elliptic equations
  • Trudinger- Moser inequality
  • Vanishing potentials

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