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http://dx.doi.org/10.14317/jami.2012.30.3_4.517

THE EXISTENCE OF TWO POSITIVE SOLUTIONS FOR $m$-POINT BOUNDARY VALUE PROBLEM WITH SIGN CHANGING NONLINEARITY  

Liu, Jian (School of Mathematical Sciences, Qufu Normal University)
Publication Information
Journal of applied mathematics & informatics / v.30, no.3_4, 2012 , pp. 517-529 More about this Journal
Abstract
In this paper, the existence theorem of two positive solutions is established for nonlinear m-point boundary value problem by using an inequality for the following third-order differential equations $$({\phi}(u^{\prime\prime}))^{\prime}+a(t)f(t,u(t))=0,\;t{\in}(0,1)$$, $${\phi}(u^{\prime\prime}(0))=\sum^{m-2}_{i=1}a_i{\phi}(u^{\prime\prime}({\xi}_i)),\;u^{\prime}(1)=0,\;u(0)=\sum^{m-2}_{i=1}b_iu({\xi}_i)$$, where ${\phi}:R{\rightarrow}R$ is an increasing homeomorphism and homomorphism and $\phi(0)=0$. The nonlinear term f may change sign, as an application, an example to demonstrate our results is given.
Keywords
m-point; Third-order; Positive solutions;
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1 D.R.Anderson, Green's function for a third-order generalized right focal problem,J.Math. Anal. Appl. 288 (2003) 1-14.   DOI
2 Y.P.Sun, Positive solutions of singular third-order three-point boundary value problem, J. Math. Anal. Appl. 306 (2005) 589-603.   DOI
3 C.L.Zhou, D.X.Ma, Existence and iteration of positive solutions for a generalized rightfocal boundary value problem with p-Laplacian operator, J. Math. Anal. Appl. 324 (2006) 409-424.   DOI
4 D.Ji, M.Feng, W.Ge, Multiple positive solutions for multipoint boundary value problems with sign changing nonlnearity, Appl. Math. Comput. 196 (2008) 515-520.
5 C.Bai, J. Fang, Existence of multiple positive solutions for nonlinear m-point boundary value problems, J.Math.Appl.Appl. 81 (2003) 76-85.
6 R.Ma, Positive solutions of nonlinear m-point boundary value problems, Comput. Math. Appl.42 (2001) 755-765.   DOI
7 Y.Sang, H.Su, Positive solutions of nonlinear third-order m-point BVP for an increasing homeomorphism and homomorphism with sign-changing nonlinearity, J.Comput.Appl.Math. 225 (2009) 288-300.   DOI
8 D.Guo, V.Lakshmikanthan, Nonlinear problems in Abstract Cones, Academic Press, San Diego, 1988.