Existence Results For Hamiltonian Elliptic Systems With Nonlinear Boundary Conditions

JULIAN FERNANDEZ BONDER; ROSSI, JULIO DANIEL

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

TEXAS STATE UNIVERSITY

Año: 1999 vol. 40 p. 1 - 15

1072-6691

We prove the existence of nontrivial solutions to the system ¢u = u; ¢v = v; on a bounded set of RN, with nonlinear coupling at the boundary given by @u=@´ = Hv; @v=@´ = 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.