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Solutions to a Three-Point Boundary Value Problem
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DOI：10.1155/2011/894135.png)
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Abstract
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By using the fixed-point index theory and Leggett-Williams fixed-point theorem, we study the existence of multiple solutions to the three-point boundary value problem u'''(t) + a(t)f(t, u(t), u'(t)) = 0, 0 < t < 1; u(0) = u'(0) = 0; u'(1) - alpha u'(eta) = lambda, where eta is an element of (0, 1/2], alpha is an element of [1/2 eta, 1/eta) are constants, lambda is an element of (0, infinity) is a parameter, and a, f are given functions. New existence theorems are obtained, which extend and complement some existing results. Examples are also given to illustrate our results.
Keywords:
POSITIVE FIXED-POINTS
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