Báo cáo hóa học: " Research Article Several Existence Theorems of Multiple Positive Solutions of Nonlinear m-Point BVP for an Increasing Homeomorphism and Homomorphism 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 Several Existence Theorems of Multiple Positive Solutions of Nonlinear m-Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 584145 19 pages doi 2009 584145 Research Article Several Existence Theorems of Multiple Positive Solutions of Nonlinear m-Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales Wei Han1 and Shugui Kang2 1 Department of Mathematics North University of China Taiyuan Shanxi 030051 China 2 Institute of Applied Mathematics Shanxi Datong University Datong Shanxi 037009 China Correspondence should be addressed to Shugui Kang dtkangshugui@ Received 24 July 2009 Accepted 29 November 2009 Recommended by Kanishka Perera By using fixed point theorems in cones the existence of multiple positive solutions is considered for nonlinear m-point boundary value problem for the following second-order boundary value problem on time scales f uA V a f f t u t 0 t e 0 T f uÁ 0 2m12 af iuNfO u T i biu ệi where f R R is an increasing homeomorphism and homomorphism and f 0 0. Some new results are obtained for the existence of twin or an arbitrary odd number of positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems respectively. In particular our criteria generalize and improve some known results by Ma and Castaneda 2001 . We must point out for readers that there is only the p-Laplacian case for increasing homeomorphism and homomorphism. As an application one example to demonstrate our results is given. Copyright 2009 W. Han and S. Kang. 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 In this paper we will be concerned with the existence of positive solutions for the following boundary value problem on time scales f uA v a t f t u t 0 t e 0 T m-2 m-2 f uh Q j aif u t i u T biu ịi i 1 i 1 where f R R is an increasing homeomorphism and homomorphism

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