Nonlinear three-point boundary value problems |
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Authors: | Abdelkader Boucherif |
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Institution: | Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912 USA |
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Abstract: | In the present work, we investigate nonlinear three-point boundary value problems (second-order differential equations with boundary conditions imposed at three consecutive points) in an effort to understand the conditions that must be imposed upon nonlinear perturbations of a linear problem in order to obtain a solution of a three-point problem. Both the noncritical case and the critical case are considered. In the first case, existence and uniqueness results are obtained, and in the second case we deal with local bifurcation problems when the nonlinearities are quadratic and cubic. |
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