Upper and lower solution method for fourth-order four-point boundary value problems

Authors:
Qin Zhang;Shihua Chen;Jinhu Lü
Affiliations:
School of Mathematics and Statistics, Wuhan University, Wuhan, PR China;School of Mathematics and Statistics, Wuhan University, Wuhan, PR China;Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 4
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Abstract

This paper is concerned with the fourth-order ordinary differential equation u(4)(t) = f(t, u(t), u"(t)), 0 t u(0) = u(1) = 0, au"(ξ1) - bu'"(ξ1) = 0, cu"(ξ2) + du'"(ξ2) = 0, where ξi ∈ [0, 1] (i = 1, 2) and a, b, c, d are nonnegative constants satisfying ad + bc + ac(ξ2 - ξ1) 0. Some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique.