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

Sérgio H.Monari Soares; Yony R.Santaria Leuyacc

doi:10.1142/S0219199717500535

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

Sérgio H.Monari Soares, Yony R.Santaria Leuyacc

Dynamical systems, differential equations and their applications

Research output: Contribution to journal › Article › peer-review

2 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 language	English
Article number	1750053
Journal	Communications in Contemporary Mathematics
Volume	20
Issue number	8
DOIs	https://doi.org/10.1142/S0219199717500535
State	Published - 1 Dec 2018

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.

Keywords

Hamiltonian elliptic systems in dimension two
exponential growth
vanishing potentials

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10.1142/S0219199717500535

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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.",

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AU - Soares, Sérgio H.Monari

AU - Leuyacc, Yony R.Santaria

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N2 - 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.

AB - 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.

KW - Hamiltonian elliptic systems in dimension two

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KW - vanishing potentials

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

Abstract

Bibliographical note

Keywords

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