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báo cáo hóa học:" Research Article Monotone Positive Solution of Nonlinear Third-Order BVP with Integral Boundary Conditions"

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: Research Article Monotone Positive Solution of Nonlinear Third-Order BVP with Integral Boundary Conditions | Hindawi Publishing Corporation Boundary Value Problems Volume 2o10 Article ID 874959 12 pages doi 10.1155 2010 874959 Research Article Monotone Positive Solution of Nonlinear Third-Order BVP with Integral Boundary Conditions Jian-Ping Sun and Hai-Bao Li Department of Applied Mathematics Lanzhou University of Technology Lanzhou Gansu 730050 China Correspondence should be addressed to Jian-Ping Sun jpsun@lut.cn Received 7 September 2010 Accepted 31 October 2010 Academic Editor Michel C. Chipot Copyright 2010 J.-P. Sun and H.-B. Li. 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. This paper is concerned with the following third-order boundary value problem with integral boundary conditions u t f t u t u t 0 t e 0 1 u 0 u 0 0 u 1 J g f u t dt where f e C 0 1 X 0 x X 0 x 0 x and g e C 0 1 0 x . By using the Guo-Krasnoselskii fixed-point theorem some sufficient conditions are obtained for the existence and nonexistence of monotone positive solution to the above problem. 1. Introduction Third-order differential equations arise in a variety of different areas of applied mathematics and physics for example in the deflection of a curved beam having a constant or varying cross section a three-layer beam electromagnetic waves or gravity driven flows and so on 1 . Recently third-order two-point or multipoint boundary value problems BVPs for short have attracted a lot of attention 2-17 . It is known that BVPs with integral boundary conditions cover multipoint BVPs as special cases. Although there are many excellent works on third-order two-point or multipoint BVPs a little work has been done for third-order BVPs with integral boundary conditions. It is worth mentioning that in 2007 Anderson and Tisdell 18 developed an interval of A values whereby a positive solution exists for the following third-order BVP with .