Electron. J. Diff. Eqns., Vol. 2004(2004), No. 46, pp. 1-12.

An application of the dual variational principle to a Hamiltonian system with discontinuous nonlinearities

Claudianor O. Alves, Daniel C. de Morais Filho, & Marco Aurelio S. Souto

Abstract:
In this article, we study the existence of solutions to the Hamiltonian elliptic system with discontinuous nonlinearities
$$\displaylines{ -\Delta u=au+bv+f(x,v), \cr -\Delta v=cu+av+g(x,u) }$$
on a bounded subset of $\mathbb{R}^n$, with zero Dirichlet boundary conditions. The functions $f$ and $g$ have a finite number of jumping discontinuities.

Submitted January 26, 2004. Published March 31, 2004.
Math Subject Classifications: 35J50, 37K05, 34A34.
Key Words: Hamiltonian systems, discontinuous nonlinearities, dual variational principle.

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Claudianor O. Alves
Departamento de Matematica e Estatistica
Universidade Federal de Campina Grande
Cx Postal 10044
58109-970-Campina Grande (PB), Brazil
email: coalves@dme.ufpb.br
Daniel C. de Morais Filho
Departamento de Matematica e Estatistica
Universidade Federal de Campina Grande
Cx Postal 10044
58109-970-Campina Grande (PB), Brazil
email: daniel@dme.ufpb.br
Marco Aurelio S. Souto
Departamento de Matematica e Estat}stica
Universidade Federal de Campina Grande
Cx Postal 10044
58109-970-Campina Grande (PB), Brazil
email: marco@dme.ufpb.br

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