Advances in Differential Equations

On nonquadratic Hamiltonian elliptic systems

D. G. De Figueiredo and C. A. Magalhães

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In this paper we prove existence of a nontrivial solution for Hamiltonian systems of the form $$ \begin{cases} -\triangle u = \delta u + \gamma v + \frac{\partial H}{\partial v} (x, u, v) \\ -\triangle v = \lambda u + \delta v + \frac{\partial H}{\partial u} (x, u, v) & \mbox{in }\;\; \Omega, \end{cases} $$ subject to Dirichlet boundary conditions. The method used is variational through a generalized mountain pass theorem for indefinite functionals due to Benci-Rabinowitz in a version introduced by Felmer

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Adv. Differential Equations, Volume 1, Number 5 (1996), 881-898.

First available in Project Euclid: 25 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J50: Variational methods for elliptic systems 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


De Figueiredo, D. G.; Magalhães, C. A. On nonquadratic Hamiltonian elliptic systems. Adv. Differential Equations 1 (1996), no. 5, 881--898.

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