On Nonquadratic Hamiltonian Elliptic Systems

In this paper we prove existence of a nontrivial solution for Hamiltonian systems of the form 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.15881898Ambrosetti, A., Rabinowitz, P.H., al variational methods in critical point theory applications (1973) J. Funct. Anal, 14, pp. 349-381Benci, V., Rabinowitz, P., Critical point theorems for indefinite functionals (1979) Invent. Math, 52, pp. 241-273Cerami, G., Un criterio de esistenza per i punti critici su varietà ilimitate (1978) Rc. Ist. Lomb. Sci. Lett, 112, pp. 332-336Clément, P.H., De Figueiredo, D.G., Mitidieri, E., Positive solutions of semilinear elliptic systems (1992) Comm. Partial Differential Equations, 17, pp. 923-940Costa, D.G., Magalhães, C.A., Un problème elliptique non-quadratique à l'infini (1992) C.R. Acad. Sci. Paris Série I, 315, pp. 1059-1062Costa, D.G., Magalhães, C.A., A variational approach to subquadratic perturbations of elliptic systems (1994) J. Differential Equations, 111, pp. 103-122Costa, D.G., Magalhães, C.A., A variational approach to noncooperative elliptic systems, , To appearde Figueiredo, D.G., Felmer, P., On superquadratic elliptic systems (1994) Trans. Amer. Math. Soc, 343, pp. 99-116Felmer, P., Periodic solutions of "superquadratic" Hamiltonian systems (1993) J. Differential Equations, 102, pp. 188-207Hulshof, J., Van Der Vorst, R., Differential systems with strongly indefinite variational structure (1993) J. Fctl. Anal, 114, pp. 32-58Landersman, E.M., Lazer, A.C., Nonlinear perturbations of linear elliptic boundary value problems at resonance (1970) J. Math. Mech., 19, pp. 609-623Mitidieri, E., Van Der Vorst, R., A strongly indefinite system with limiting exponent, , to appearRabinowitz, P., Minimax methods in critical point theory with applications to differential equations CBMS Regional Conf. Ser. in Math. Amer. Math. Soc., 65. , Providenc