An application of the dual variational principle to a Hamiltonian system with discontinuous nonlinearities - Claudianor Oliveira Alves; Daniel C. De Morais Filho; Marco Aurelio S. Souto (Electronic Journal of Differential Equations, 2004)
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 $mathbbR^n$, with zero Dirichlet boundary conditions. The functions $f$ and $g$ have a finite number of jumping discontinuities.