On 2nth-order nonlinear multi-point boundary value problems

Authors:
Yuan-Ming Wang
Affiliations:
Department of Mathematics, East China Normal University, Shanghai 200241, People's Republic of China and Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Sci ...
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

Citing 6
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Abstract

This paper is concerned with the existence and uniqueness of a solution for a class of 2nth-order nonlinear multi-point boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone condition on the nonlinear function. A sufficient condition for the uniqueness of a solution is given. It is also shown that there exist two sequences which converge monotonically from above and below, respectively, to the unique solution. Two examples are presented to illustrate the results.