TAILIEUCHUNG - Báo cáo sinh học: " Research Article Inequalities among Eigenvalues of Second-Order Symmetric Equations on Time Scales"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Inequalities among Eigenvalues of Second-Order Symmetric Equations on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 317416 24 pages doi 2010 317416 Research Article Inequalities among Eigenvalues of Second-Order Symmetric Equations on Time Scales Chao Zhang and Shurong Sun School of Science University of Jinan Jinan Shandong 250022 China Correspondence should be addressed to Chao Zhang ss_zhangc@ Received 28 January 2010 Revised 2 May 2010 Accepted 5 May 2010 Academic Editor A. Pankov Copyright 2010 C. Zhang and S. Sun. 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. We consider coupled boundary value problems for second-order symmetric equations on time scales. Existence of eigenvalues of this boundary value problem is proved numbers of their eigenvalues are calculated and their relationships are obtained. These results not only unify the existing ones of coupled boundary value problems for second-order symmetric differential equations but also contain more complicated time scales. 1. Introduction In this paper we consider the following second-order symmetric equation - p t yA t q t y t Xr t yơ t t e p 0 p 1 n T and 0 1 e T L1 with the coupled boundary conditions y 1 uK y pw yA p 0 where T is a time scale p q and r are real and continuous functions in p 0 p 1 nT p 0 over p 0 1 n T r 0 over p 0 p 1 n T and p p 0 p 1 1 Ơ t and p t are the 2 Advances in Difference Equations forward and backward jump operators in T yA is the delta derivative and yơ f y ơ f 0 0 -n 0 n is a constant parameter i V-1 K kn kD2 kij e R i j 1 2 with detK 1. k21 k22 1-3 The boundary condition contains the two special cases the periodic and antiperiodic conditions. In fact is the periodic boundary condition in the case where 0 0 and K I the identity matrix and is the antiperiodic condition in the case where 0 n and K I. .

• Sinh học
• Báo cáo sinh học hay
• cách trình bày báo cáo
• báo cáo sinh học
• công trình nghiên cứu sinh học
• tài liệu về sinh học