We prove existence of variational solutions for the Hamiltonian coupling of nonlinear Schrödinger equations in the whole plane, when the nonlinearities exhibit supercritical growth with respect to the Trudinger–Moser inequality. We discover linking type solutions which have finite energy in a suitable Lorentz–Sobolev space setting.
Existence of solitary waves for supercritical Schrödinger systems in dimension two / D. Cassani, C. Tarsi. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 54:2(2015), pp. 1673-1704.
Existence of solitary waves for supercritical Schrödinger systems in dimension two
C. TarsiUltimo
2015
Abstract
We prove existence of variational solutions for the Hamiltonian coupling of nonlinear Schrödinger equations in the whole plane, when the nonlinearities exhibit supercritical growth with respect to the Trudinger–Moser inequality. We discover linking type solutions which have finite energy in a suitable Lorentz–Sobolev space setting.
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