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In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter $\begin{array}{*{20}c} {u''\left( t \right) + \lambda f\left( {t,u} \right) = 0} & {t \in \left( {0,1} \right),} \\ {u'\left( 0 \right) = \sum\limits_{i = 1}^{m - 2} {b_i u'} \left( {\xi _i } \right),} & {u\left( 1 \right) = \sum\limits_{i = 1}^{m - 2} {a_i u\left( {\xi _i } \right),} } \\ \end{array}$ where λ > 0 is a parameter, 0 < ξ 1 < ξ 2 < … < ξ m−2 < 1 with $0 < \sum\limits_{i = 1}^{m - 2} {a_i < 1, \sum\limits_{i = 1}^{m - 2} {b_i < 1, a_i , b_i \in \left[ {0,\infty } \right)} }$ and f(t, u) ≥ − M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Nov 14, 2009
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