caa a22 4500 445830654 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10255-009-6180-3 doi (NATIONALLICENCE)springer-10.1007/s10255-009-6180-3 Multiple positive solutions for semi-positone m -point boundary value problems [Elektronische Daten] [Cheng-bo Zhai, Cheng Yang] 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. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer Berlin Heidelberg, 2011 Multiple positive solutions nationallicence cone nationallicence semi-positone m -point boundary value problem nationallicence concave functional nationallicence parameter nationallicence Zhai Cheng-bo School of Mathematical Science, Shanxi University, 030006, Shanxi, China aut Yang Cheng Business College of Shanxi University, 030031, Shanxi, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 419-426 0168-9673 27:3<419 2011 27 10255 https://doi.org/10.1007/s10255-009-6180-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-009-6180-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhai Cheng-bo School of Mathematical Science, Shanxi University, 030006, Shanxi, China aut NATIONALLICENCE 700 1- Yang Cheng Business College of Shanxi University, 030031, Shanxi, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 419-426 0168-9673 27:3<419 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer