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1996 On nonquadratic Hamiltonian elliptic systems
D. G. De Figueiredo, C. A. Magalhães
Adv. Differential Equations 1(5): 881-898 (1996).

Abstract

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

Citation

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D. G. De Figueiredo. C. A. Magalhães. "On nonquadratic Hamiltonian elliptic systems." Adv. Differential Equations 1 (5) 881 - 898, 1996.

Information

Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0857.35043
MathSciNet: MR1392009

Subjects:
Primary: 35J60
Secondary: 35J50 , 58E05

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.1 • No. 5 • 1996
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