The iterative solutions of 2nth-order nonlinear multi-point boundary value problems |
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| Authors: | Yuan-Ming Wang |
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| Institution: | Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai 200234, People’s Republic of China |
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| Abstract: | The aim of this paper is to investigate the existence of iterative solutions for a class of 2nth-order nonlinear multi-point boundary value problems. The multi-point boundary condition under consideration includes various commonly discussed boundary conditions, such as three- or four-point boundary condition, (n + 2)-point boundary condition and 2(n − m)-point boundary condition. The existence problem is based on the method of upper and lower solutions and its associated monotone iterative technique. A monotone iteration is developed so that the iterative sequence converges monotonically to a maximal solution or a minimal solution, depending on whether the initial iteration is an upper solution or a lower solution. Two examples are presented to illustrate the results. |
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| Keywords: | 2nth-order equation Nonlinear multi-point boundary value problem Iterative solution Method of upper and lower solutions Monotone iteration |
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