Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

Sergio H. Monari Soares and Yony R. Santaria Leuyacc

Mathematische Nachrichten, 2019, vol. 292, issue 1, 137-158

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.

Date: 2019
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