A Neumann problem for a system depending on the unknown boundary values of the solution

作者：Amster Pablo^*; Deboli Alberto

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2013, (2): 1-11.

• Two-ion electro-diffusion models
• Landesman-Lazer conditions
• nonlinear systems
• topological degree

A semilinear system of second order ODEs under Neumann conditions is studied. The system has the particularity that its nonlinear term depends on the (unknown) Dirichlet values y(0) and y(1) of the solution. Asymptotic and non-asymptotic sufficient conditions of Landesman-Lazer type for existence of solutions are given. We generalize our previous results for a scalar equation, and a well known result by Nirenberg for a standard nonlinearity independent of y(0) and y(1).

• 出版日期2013