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báo cáo hóa học:" Research Article Time-Scale-Dependent Criteria for the Existence of Positive Solutions to p-Laplacian Multipoint Boundary Value Problem"

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 Time-Scale-Dependent Criteria for the Existence of Positive Solutions to p-Laplacian Multipoint Boundary Value Problem | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 746106 20 pages doi 10.1155 2010 746106 Research Article Time-Scale-Dependent Criteria for the Existence of Positive Solutions to p-Laplacian Multipoint Boundary Value Problem Wenyong Zhong1 and Wei Lin2 1 School of Mathematics and Computer Sciences Jishou University Hunan 416000 China 2 Shanghai Key Laboratory of Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China Correspondence should be addressed to Wei Lin wlin@fudan.edu.cn Received 1 May 2010 Revised 23 July 2010 Accepted 30 July 2010 Academic Editor Alberto Cabada Copyright 2010 W. Zhong and W. Lin. 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. By virtue of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem we analytically establish several sufficient criteria for the existence of at least two or three positive solutions in the p-Laplacian dynamic equations on time scales with a particular kind of p-Laplacian and rn-point boundary value condition. It is this kind of boundary value condition that leads the established criteria to be dependent on the time scales. Also we provide a representative and nontrivial example to illustrate a possible application of the analytical results established. We believe that the established analytical results and the example together guarantee the reliability of numerical computation of those p-Laplacian and rn-point boundary value problems on time scales. 1. Introduction The investigation of dynamic equations on time scales originally attributed to Stefan Hilger s seminal work 1 2 two decades ago is now undergoing a rapid development. It not only unifies the existing results and principles for both differential equations and difference equations