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Boundary value problems with compatible boundary conditions

George L. KarakostasP. K. Palamides — 2005

Czechoslovak Mathematical Journal

If Y is a subset of the space n × n , we call a pair of continuous functions U , V Y -compatible, if they map the space n into itself and satisfy U x · V y 0 , for all ( x , y ) Y with x · y 0 . (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential n -dimensional system is investigated, provided the boundary conditions are given via a pair of compatible mappings. By using a truncation of the initial equation and restrictions of its domain, Brouwer’s...

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