Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
Date
1999-10-07
Authors
Fernandez Bonder, Julian
Pinasco, Juan Pablo
Rossi, Julio D.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Elliptic systems, Nonlinear boundary conditions, Variational problems
Citation
Bonder, 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.
Rights
Attribution 4.0 International