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

P. AMSTER; A. DÉBOLI

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

UNIV SZEGED

Año: 2012

1417-3875

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 nonlinearity independent of y(0) and y(1).