On nonquadratic Hamiltonian elliptic systems
The authors prove existence of a nontrivial solution for a Hamiltonian system of the form \[ -\Delta u=\delta u+\gamma v+{{\partial H}\over{\partial v}}(x,u,v), \quad -\Delta v=\lambda u+\delta v+{{\partial H}\over{\partial u}}(x,u,v), \qquad\text{in }\Omega, \] subject to Dirichlet boundary conditions. The method used is a generalized mountain pass theorem for indefinite functionals due to Benci-Rabinowitz in a version introduced by Felmer.
scientific article; zbMATH DE number 896503