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Singular Hamiltonian elliptic systems with critical exponential growth in dimension two
Author(s) -
Monari Soares Sergio H.,
Santaria Leuyacc Yony R.
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700215
Subject(s) - mathematics , bounded function , lorentz transformation , exponential growth , hamiltonian (control theory) , pure mathematics , exponential function , sobolev space , hamiltonian system , mathematical analysis , quantum mechanics , mathematical optimization , physics
We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system− Δ u + V ( x ) u =g ( v )| x | a,x ∈ R 2 ,− Δ v + V ( x ) v =f ( u )| x | b,x ∈ R 2 ,where a , b are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on R 2 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.