Báo cáo hóa học: " Research Article Multiple Positive Solutions of m-Point BVPs for Third-Order p-Laplacian Dynamic Equations on Time Scales"

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 Multiple Positive Solutions of m-Point BVPs for Third-Order p-Laplacian Dynamic Equations on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 262857 12 pages doi 2009 262857 Research Article Multiple Positive Solutions of m-Point BVPs for Third-Order p-Laplacian Dynamic Equations on Time Scales Li-Hua Bian 1 Xi-Ping He 1 2 and Hong-Rui Sun1 1 School of Mathematics and Statistics Lanzhou University Lanzhou Gansu 730000 China 2 Center of Teaching Guidance Gansu Radio and TV University Lanzhou Gansu 730000 China Correspondence should be addressed to Hong-Rui Sun hrsun@ Received 17 August 2009 Accepted 26 October 2009 Recommended by Alberto Cabada This paper is concerned with the existence of multiple positive solutions for the third-order p-Laplacian dynamic equation fp uAV t V a f f t u t uA t 0 t e 0 T T with the multipoint boundary conditions uA 0 uAV 0 0 u T B0 -2 b uA fi 0 where fp ù u p-2u with p 1. Using the fixed point theorem due to Avery and Peterson we establish the existence criteria of at least three positive solutions to the problem. As an application an example is given to illustrate the result. The interesting points are that not only do we consider third-order p-Laplacian dynamic equation but also the nonlinear term f is involved with the first-order delta derivative of the unknown function. Copyright 2009 Li-Hua Bian 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 The theory of dynamic equations on time scales was introduced by Stefan Hilger in 1988 1 . This theory has attracted many researchers attention and interest since it cannot only unify differential and difference equations but also provides accurate information of phenomena that manifest themselves partly in continuous time and partly in discrete time. In addition time-scale calculus would allow exploration of a variety of situations in economic

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