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 Existence of Solutions for Nonlinear Four-Point p-Laplacian Boundary Value Problems on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 123565 20 pages doi 2009 123565 Research Article Existence of Solutions for Nonlinear Four-Point p-Laplacian Boundary Value Problems on Time Scales S. Gulsan Topal O. Batit Ozen and Erbil Cetin Department of Mathematics Ege University Bornova 35100 Izmir Turkey Correspondence should be addressed to S. Gulsan Topal Received 16 March 2009 Accepted 20 July 2009 Recommended by Alberto Cabada We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a p-Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for p-Laplacian boundary value problem is also given by the monotone method. Copyright 2009 S. Gulsan Topal et al. 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 Let T be any time scale such that 0 1 be subset of T. The concept of dynamic equations on time scales can build bridges between differential and difference equations. This concept not only gives us unified approach to study the boundary value problems on discrete intervals with uniform step size and real intervals but also gives an extended approach to study on discrete case with non uniform step size or combination of real and discrete intervals. Some basic definitions and theorems on time scales can be found in 1 2 . In this paper we study the existence of positive solutions for the following nonlinear four-point boundary value problem with a p-Laplacian operator ộp xA V t h t f t x t 0 t e 0 1 aộp x p 0 -y ộp x g 0 Yộp x ơ 1 ôộp xAn 0 L2 where ộp s is an operator that is ộp s s p 2s for p 1 ộp 1 s ộq s where 1 p 1 q 1 a Y 0 Ỗ 0 ị n e p 0 ơ 1 with ị n 2
