The Method of upper and lower solutions for second-order non-homogeneous two-point boundary-value problem
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This paper studies the existence and uniqueness of solutions for a type of second-order two-point boundary-value problem depending on the first-order derivative through a non-linear term. By constructing a special cone and using the upper and lower solutions method, we obtain the sufficient conditions of the existence and uniqueness of solutions, and a monotone iterative sequence solving the boundary-value problem. An error estimate formula is also given under the condition of a unique solution.
CitationJia, M., & Liu, X. (2007). The Method of upper and lower solutions for second-order non-homogeneous two-point boundary-value problem. Electronic Journal of Differential Equations, 2007(116), pp. 1-10.
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