Hamiltonian elliptic systems in dimension two with potentials which can vanish at infinity

Sérgio H.Monari Soares, Yony Raul Santaria Leuyacc

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1 Scopus citations

Abstract

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system {-Δu + V (x)u = g(v), x ∈ R2, - Δv + V (x)v = f(u), x ∈ R2, where V is a positive function which can vanish at infinity and be unbounded from above and f and g have exponential growth range. The proof involves a truncation argument combined with the linking theorem and a finite-dimensional approximation.

Original languageEnglish
Article number1750053
JournalCommunications in Contemporary Mathematics
Volume20
Issue number8
DOIs
StatePublished - 1 Dec 2018
Externally publishedYes

Bibliographical note

Funding Information:
S. H. M. Soares was partially supported by CNPq/Brazil. Y. R. S. Leuyacc was supported by PROEX/CAPES/Brazil.

Publisher Copyright:
© 2018 World Scientific Publishing Company.

Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

Keywords

  • Hamiltonian elliptic systems in dimension two
  • exponential growth
  • vanishing potentials

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