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

Pablo Amster | Zendy; Alberto Déboli | Zendy

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

Author(s) -

Pablo Amster,

Alberto Déboli

Publication year - 2013

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2013.1.2

Subject(s) - mathematics , neumann boundary condition , boundary value problem , boundary (topology) , von neumann architecture , pure mathematics , mathematical analysis

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).

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