Báo cáo hóa học: " Research Article The Existence of Positive Solutions for Third-Order p-Laplacian m-Point Boundary Value Problems with Sign Changing Nonlinearity 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 The Existence of Positive Solutions for Third-Order p-Laplacian m-Point Boundary Value Problems with Sign Changing Nonlinearity on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 169321 14 pages doi 2009 169321 Research Article The Existence of Positive Solutions for Third-Order p-Laplacian m-Point Boundary Value Problems with Sign Changing Nonlinearity on Time Scales Fuyi Xu and Zhaowei Meng School of Science Shandong University of Technology Zibo Shandong 255049 China Correspondence should be addressed to Fuyi Xu xfy_02@ Received 25 February 2009 Revised 10 April 2009 Accepted 2 June 2009 Recommended by Alberto Cabada We study the following third-order p-Laplacian m-point boundary value problems on time scales fp mav V a f f t U t 0 t e 0 T t u 0 2bi-uttf u T 0 fp uAV 0 Sm12Cifp uáv ỉi where fp s is p-Laplacian operator that is fp s s p-2s p 1 f-1 fq 1 p 1 q 1 0 21 ịm-2 pfT . We obtain the existence of positive solutions by using fixed-point theorem in cones. In particular the nonlinear term f t u is allowed to change sign. The conclusions in this paper essentially extend and improve the known results. Copyright 2009 F. Xu and Z. Meng. 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 time scales was initiated by Hilger 1 as a mean of unifying and extending theories from differential and difference equations. The study of time scales has lead to several important applications in the study of insect population models neural networks heat transfer and epidemic models see for example 2-6 . Recently the boundary value problems with p-Laplacian operator have also been discussed extensively in literature for example see 7-18 . However to the best of our knowledge there are not many results concerning the higher-order p-Laplacian mutilpoint boundary value problem on time scales. A time scale T is a nonempty closed subset of R. We make the blanket assumption

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