Existence and approximation of solutions for nonlinear second-order four-point boundary value problems |
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Authors: | Libo Wang Minghe Pei Weigao Ge |
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Institution: | aDepartment of Mathematics, Beihua University, Ji’lin 132013, PR China;bDepartment of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China |
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Abstract: | Applying the method of upper and lower solutions, Leray–Schauder degree theory and one-sided Nagumo condition, we obtain the existence and uniqueness results for a class of nonlinear second-order four-point boundary value problems. By the generalized approximation method, a monotone iteration sequence which converges uniformly to the unique solution of the nonlinear problem and converges quadratically to the unique solution of the linear problem is also obtained. |
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Keywords: | The method of upper and lower solutions Leray– Schauder degree theory One-sided Nagumo condition The generalized approximation method |
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