tailieunhanh - Báo cáo hoa học: " Research Article A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems"

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 A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 671625 15 pages doi 2009 671625 Research Article A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems Ruyun Ma Youji Xu and Chenghua Gao Department of Mathematics Northwest Normal University Lanzhou Gansu 730070 China Correspondence should be addressed to Ruyun Ma mary@ Received 12 February 2009 Accepted 20 August 2009 Recommended by Svatoslav Stanek Let T e N be an integer with T 1 T 1 . T T 0 1 . T 1 . We consider boundary value problems of nonlinear second-order difference equations of the form A2u t - 1 Xa f f u t 0 t e T u 0 u T 1 0 where a T R f e C 0 to 0 to and f s 0 for s 0 and f0 fTO 0 f0 lims 0 f s s fTO lims TOf s s. We investigate the global structure of positive solutions by using the Rabinowitz s global bifurcation theorem. Copyright 2009 Ruyun Ma 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 Let T e N be an integer with T 1 T 1 . T T 0 1 . T 1 . We study the global structure of positive solutions of the problem A2u t - 1 Xa t f uftf 0 t e T J . u 0 u T 1 0. Here A is a positive parameter a T R and f 0 to 0 to are continuous. Denote f0 lims 0 f s s and to lims TOf s s. There are many literature dealing with similar difference equations subject to various boundary value conditions. We refer to Agarwal and Henderson 1 Agarwal and O Regan 2 Agarwal and Wong 3 Rachunkova and Tisdell 4 Rodriguez 5 Cheng and Yen 6 Zhang and Feng 7 R. Ma and H. Ma 8 Ma 9 and the references therein. These results were usually obtained by analytic techniques various fixed point theorems and global bifurcation techniques. For example in 8 the authors investigated the global structure 2 Advances in Difference Equations of .