tailieunhanh - Báo cáo hóa học: " Research Article Eigenvalue Problems for Systems of Nonlinear Boundary Value 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: Research Article Eigenvalue Problems for Systems of Nonlinear Boundary Value Problems on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2007 Article ID 31640 10 pages doi 2007 31640 Research Article Eigenvalue Problems for Systems of Nonlinear Boundary Value Problems on Time Scales M. Benchohra J. Henderson and S. K. Ntouyas Received 28 June 2007 Accepted 19 November 2007 Recommended by Kanishka Perera Values of A are determined for which there exist positive solutions of the system of dynamic equations uAA t Aa t f v ơ t 0 vAA t Ab t g u a t 0 for t G 0 1 t satisfying the boundary conditions u 0 0 u ơ2 1 v 0 0 v ơ2 1 where T is a time scale. A Guo-Krasnosel skii fixed point-theorem is applied. Copyright 2007 M. Benchohra 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 be a time scale with 0 ơ2 1 G T. Given an interval J of R we will use the interval notation Jt J n T. We are concerned with determining values of A eigenvalues for which there exist positive solutions for the system of dynamic equations uAA t Aa t f v ơ t 0 t G 0 1 t vAA t Ab t g u ff t 0 t G 0 1 t satisfying the boundary conditions u 0 0 u ơ2 1 v 0 0 v ơ2 1 2 Advances in Difference Equations where a f g G C 0 oo 0 ro b a b G C 0 Ơ 1 t 0 0 and each does not vanish identically on any closed subinterval of 0 Ơ 1 t c all of f0 lim . .f x x g0 limx 0 g x x fx limx f x x and g- limx .-Jg x x exist as real numbers. There is an ongoing flurry of research activities devoted to positive solutions of dynamic equations on time scales see . 1 7 . This work entails an extension of the paper by Chyan and Henderson 8 to eigenvalue problems for systems of nonlinear boundary value problems on time scales. Also in that light this paper is closely related to the works of Li and Sun 9 10 . On a larger scale there has been a great deal of study focused on positive solutions