Multipoint boundary value problems for nonlinear ordinary differential equations |
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Authors: | Jesú s Rodriguez,Padraic Taylor |
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Affiliation: | 1. Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695-8205, United States;2. Department of Mathematics and Statistics, Youngstown State University, One University Plaza, Youngstown, OH 44555, United States |
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Abstract: | In this paper we provide sufficient conditions for the existence of solutions to multipoint boundary value problems for nonlinear ordinary differential equations. We consider the case where the solution space of the associated linear homogeneous boundary value problem is less than 2. When this solution space is trivial, we establish existence results via the Schauder Fixed Point Theorem. In the resonance case, we use a projection scheme to provide criteria for the solvability of our nonlinear boundary value problem. We accomplish this by analyzing a link between the behavior of the nonlinearity and the solution set of the associated linear homogeneous boundary value problem. |
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Keywords: | 34B10 34B15 |
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