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Báo cáo hóa học: " Research Article Existence of Positive Solutions in Generalized Boundary Value Problem for p-Laplacian "

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 Positive Solutions in Generalized Boundary Value Problem for p-Laplacian | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 848191 19 pages doi 10.1155 2009 848191 Research Article Existence of Positive Solutions in Generalized Boundary Value Problem for p-Laplacian Dynamic Equations on Time Scales Wenyong Zhong1 2 and Wei Lin1 1 Research Center and Key Laboratory of Mathematics for Nonlinear Sciences School of Mathematical Sciences Fudan University Shanghai 200433 China 2 School of Mathematics and Computer Sciences Jishou University Hunan 416000 China Correspondence should be addressed to Wei Lin wlin@fudan.edu.cn Received 31 March 2009 Accepted 7 May 2009 Recommended by Alberto Cabada We analytically establish the conditions for the existence of at least two or three positive solutions in the generalized rn-point boundary value problem for the p-Laplacian dynamic equations on time scales by means of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem. Furthermore we illustrate the possible application of our analytical results with a concrete and nontrivial dynamic equation on specific time scales. Copyright 2009 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. 1. Introduction Since the seminal work by Stefan Hilger in 1988 there has been a rapid development in the research of dynamic equations on time scales. The gradually maturing theory of dynamic equations not only includes the majority of the existing analytical results on both differential equations and difference equations with uniform time-steps but also establishes a solid foundation for the research of hybrid equations on different kinds of time scales. More importantly with this foundation and those ongoing investigations concrete applications of dynamic equations on time scales in mathematical modeling of real processes and .