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Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

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  • Sergio H. Monari Soares
  • Yony R. Santaria Leuyacc

Abstract

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system −Δu+V(x)u=g(v)|x|a,x∈R2,−Δv+V(x)v=f(u)|x|b,x∈R2,where a,b are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on R2 by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.

Suggested Citation

  • Sergio H. Monari Soares & Yony R. Santaria Leuyacc, 2019. "Singular Hamiltonian elliptic systems with critical exponential growth in dimension two," Mathematische Nachrichten, Wiley Blackwell, vol. 292(1), pages 137-158, January.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:1:p:137-158
    DOI: 10.1002/mana.201700215
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