Fernandez Bonder, JulianPinasco, Juan PabloRossi, Julio D.2019-11-212019-11-211999-10-07Bonder, J. F., Pinasco, J. P., & Rossi, J. D. (1999). Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions. <i>Electronic Journal of Differential Equations, 1999</i>(40), pp. 1-15.1072-6691https://hdl.handle.net/10877/8854We prove the existence of nontrivial solutions to the system Δu = u, Δv = v, on a bounded set of ℝN, with nonlinear coupling at the boundary given by ϑu / ϑn = Hv, ϑv / ϑn = Hu. The proof is done under suitable assumptions on the Hamiltonian H, and based on a variational argument that is a generalization of the mountain pass theorem. Under further assumptions on the Hamiltonian, we prove the existence of positive solutions.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalElliptic systemsNonlinear boundary conditionsVariational problemsArticle