Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Monotone and convex positive solutions for fourth-order multi-point boundary value problems | Liu et al. Boundary Value Problems 2011 2011 21 http content 2011 1 21 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Monotone and convex positive solutions for fourth-order multi-point boundary value problems Yang Liu1 2 Zhang Weiguo 1 and Shen Chunfang2 Correspondence yliu1219@163. com 1College of Science University of Shanghai for Science and Technology Shanghai 200093 PR China Full list of author information is available at the end of the article Springer Abstract The existence results of multiple monotone and convex positive solutions for some fourth-order multi-point boundary value problems are established. The nonlinearities in the problems studied depend on all order derivatives. The analysis relies on a fixed point theorem in a cone. The explicit expressions and properties of associated Green s functions are also given. MSC 34B10 34B15. Keywords multi-point boundary value problem positive solution cone fixed point 1 Introduction Boundary value problems for second and higher order nonlinear differential equations play a very important role in both theory and applications. For example the deformations of an elastic beam in the equilibrium state can be described as a boundary value problem of some fourth-order differential equations. Owing to its importance in application the existence of positive solutions for nonlinear second and higher order boundary value problems has been studied by many authors. We refer to recent contributions of Ma 1-3 He and Ge 4 Guo and Ge 5 Avery et al. 6 7 Henderson 8 Eloe and Henderson 9 Yang et al. 10 Webb and Infante 11 12 and Agarwal and O Regan 13 . For survey of known results and additional references we refer the reader to the monographs by Agarwal 14 and Agarwal et al. 15 . When it comes to positive solutions for nonlinear fourth-order ordinary differential equations two point boundary value problems are studied extensively see 16-24 . Few papers deal with the .
