tailieunhanh - Báo cáo hóa học: "SECOND-ORDER n-POINT EIGENVALUE PROBLEMS 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: SECOND-ORDER n-POINT EIGENVALUE PROBLEMS ON TIME SCALES | SECOND-ORDER n-POINT EIGENVALUE PROBLEMS ON TIME SCALES DOUGLAS R. ANDERSON AND RUYUN MA Received 10 December 2004 Revised 3 November 2005 Accepted 6 November 2005 We discuss conditions for the existence of at least one positive solution to a nonlinear second-order Sturm-Liouville-type multipoint eigenvalue problem on time scales. The results extend previous work on both the continuous case and more general time scales and are based on the Guo-Krasnosel skii fixed point theorem. Copyright 2006 D. R. Anderson and R. Ma. 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 We are interested in the second-order multipoint time-scale eigenvalue problem pyv A t -q t y t hh t f y 0 t1 t tn n-1 n-1 ay t1 - p t1 yj t1 y aiy ti yy tn 8p tn yj tn y biy ti zX1 r ỉ X 1 y 1 I y X n f 1 X n Ì y X n izXi - X J i 2 i 2 where p q t1 tn 0 to p G CA t1 tn q G C t1 tn the points ti G T for i G 1 2 . n with t1 t2 tn a p y s G 0 to ay aS Ịỉy 0 ai bi G 0 to i g 2 . n - 1 . The continuous function f 0 to 0 to is such that the following exist f0 lim f fTO lim f y-0 y y-TO y Hindawi Publishing Corporation Advances in Difference Equations Volume 2006 Article ID 59572 Pages 1-17 DOI ADE 2006 59572 2 Second-order M-point eigenvalue problems on time scales and the right-dense continuous function h t1 tn 0 to satisfies some suitable conditions to be developed. Problem is a generalization to time scales of the problem when T is restricted to R on the unit interval in Ma and Thompson 19 and extends the type of time-scale boundary value problem found in Anderson 2 Atici and Guseinov 6 Kaufmann 15 Kaufmann and Raffoul 16 and Sun and Li 21 22 . Other related three-point problems on time scales include Anderson and Avery 4 Anderson et al. 5 Peterson etal. 20 and a singular problem in .