Advances in Differential Equations

On a class of Hamiltonian systems with Trudinger-Moser nonlinearities

Wilberclay G. Melo and Manassés de Souza

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In the present paper, we study existence of nontrivial weak solutions for a class of Hamiltonian systems of type \begin{align} \left \{ \begin{array}{ll} -\Delta u +b(x) u = w_{1}(x)f_{1}(v), & v > 0; \\ -\Delta v +b(x) v =w_{2}(x)f_{2}(u), & u > 0 , \end{array} \right . \end{align} where $b:\mathbb{R}^2 \rightarrow \mathbb{R}$ is a continuous potential which may change sign and the nonlinearity $f_{i}:\mathbb{R} \rightarrow \mathbb{R}$ has critical or subcritical exponential growth in the sense of Trudinger-Moser's inequality, for $i=1,2$. The main results are proved by using variational methods through strongly indefinite functionals.

Article information

Adv. Differential Equations, Volume 20, Number 3/4 (2015), 233-258.

First available in Project Euclid: 4 February 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J50: Variational methods for elliptic systems 35J55 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]


de Souza, Manassés; Melo, Wilberclay G. On a class of Hamiltonian systems with Trudinger-Moser nonlinearities. Adv. Differential Equations 20 (2015), no. 3/4, 233--258.

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