Singular Hamiltonian elliptic systems with critical exponential growth in dimension two
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...
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| Veröffentlicht in: | Mathematische Nachrichten 2019-01, Vol.292 (1), p.137-158 |
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| creator | Monari Soares, Sergio H. Santaria Leuyacc, Yony R. |
| description | 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. |
| doi_str_mv | 10.1002/mana.201700215 |
| format | Article |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | 35J75 Secondary: 35J50 critical exponential growth Primary: 35J15 singular Hamiltonian elliptic systems Sobolev space Trudinger–Moser inequalities in Lorentz–Sobolev spaces |
| title | Singular Hamiltonian elliptic systems with critical exponential growth in dimension two |
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