Abstract
Under certain conditions on the nonlinearity f and by using Leray–Schauder nonlinear alternative and the Banach contraction theorem, we prove the existence and uniqueness of nontrivial solution of the following third-order three-point boundary value problem (BVP1):
then we study the positivity by applying the well-known Guo–Krasnosel’skii fixed-point theorem. The interesting point lies in the fact that the nonlinear term is allowed to depend on the first-order derivative u ′.
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Guezane-Lakoud, A., Zenkoufi, L. (2013). Study of Third-Order Three-Point Boundary Value Problem with Dependence on the First-Order Derivative. In: Anastassiou, G., Duman, O. (eds) Advances in Applied Mathematics and Approximation Theory. Springer Proceedings in Mathematics & Statistics, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6393-1_28
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DOI: https://doi.org/10.1007/978-1-4614-6393-1_28
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