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 The Monotone Iterative Technique for Three-Point Second-Order Integrodifferential Boundary Value Problems with p-Laplacian | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 57481 9 pages doi 2007 57481 Research Article The Monotone Iterative Technique for Three-Point Second-Order Integrodifferential Boundary Value Problems with p-Laplacian Bashir Ahmad and Juan J. Nieto Received 18 December 2006 Revised 1 February 2007 Accepted 23 April 2007 Recommended by Donal O Regan A monotone iterative technique is applied to prove the existence of the extremal positive pseudosymmetric solutions for a three-point second-order p-Laplacian integrodifferential boundary value problem. Copyright 2007 B. Ahmad and J. J. Nieto. 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. 1. Introduction Investigation of positive solutions of multipoint second-order ordinary boundary value problems initiated by Il in and Moiseev 1 2 has been extensively addressed by many authors for instance see 3-6 . Multipoint problems refer to a different family of boundary conditions in the study of disconjugacy theory 7 . Recently Eloe and Ahmad 8 addressed a nonlinear nth-order BVP with nonlocal conditions. Also there has been a considerable attention on p-Laplacian BVPs 9-18 as p-Laplacian appears in the study of flowthrough porous media p 3 2 nonlinear elasticity p 2 glaciology 1 p 4 3 and so forth. In this paper we develop a monotone iterative technique to prove the existence of extremal positive pseudosymmetric solutions for the following three-point second-order p-Laplacian integrodifferential boundary value problem BVP c . f 1 n 2 . p x t a t f t x t K t Z x Z 1 0 t e 0 1 t x 0 0 x n x 1 0 n 1 where p 1 typ s s s p 2. Let yq be the inverse of typ. 2 Boundary Value Problems In passing we note that the monotone iterative technique developed in this paper is an application of Amann s method 19 and the first term of the .
