Solutions for m-Point BVP with Sign Changing Nonlinearity

Hua Su School of Statistics and Mathematic, Shandong University of Finance, Jinan, Shandong 250014, China Correspondence should be addressed to Hua Su, [email protected] Received 24 October 2008; Accepted 31 January 2009 Recommended by Binggen Zhang We study the existence of positive solutions for the following nonlinear m-point boundary value problem for an increasing homeomorphism and homomorphism with sign changing nonlinearity: { φ u′ t ′ a t f t, u t 0, 0 < t < 1, u′ 0 ∑m−2 i 1 aiu′ ξi , u 1 ∑k i 1biu ξi − ∑s i k 1biu ξi − ∑m−2 i s 1biu ′ ξi , where φ : R → R is an increasing homeomorphism and homomorphism and φ 0 0. The nonlinear term f may change sign. As an application, an example to demonstrate our results is given. The conclusions in this paper essentially extend and improve the known results. Copyright q 2009 Hua Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.