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Positive Solutions of Third Order Boundary Value Problems

Abdelkader Boucherif

Abstract


We investigate the existence of positive solutions of third order boundary value problems with changing sign Carath´eodory nonlinearities of the form. We provide simple sufficient conditions on the nonlinearity f in order to obtain a priori bounds on solutions of a one parameter family of problems, related to the original one. We then rely on the topological transversality theorem to prove the existence of positive solutions of the given problem. As a byproduct, we shall obtain a multiplicity result.

Keywords


Third order differential equations, three-point boundary value problems, a priori bound on solutions, positive solutions, Granas topological transversality theorem.

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