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Báo cáo hóa học: " Research Article Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions"

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 Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 347291 18 pages doi 10.1155 2009 347291 Research Article Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions Chao Zhang and Shurong Sun School of Science University of Jinan Jinan Shandong 250022 China Correspondence should be addressed to Chao Zhang ss_zhangc@Lijn.edii.cn Received 11 February 2009 Accepted 11 May 2009 Recommended by Johnny Henderson This paper studies general coupled boundary value problems for second-order difference equations. Existence of eigenvalues is proved numbers of their eigenvalues are calculated and their relationships between the eigenvalues of second-order difference equation with three different coupled boundary conditions are established. Copyright 2009 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. 1. Introduction Consider the second-order difference equation -v Pnàyn qnyn AWnyn n e 0 N - 1 1.1 with the general coupled boundary condition yN-1 AyN-1 eiaK y-1 Ay-1 1.2 where N 2 is an integer A is the forward difference operator Ayn yn 1 - yn V is the backward difference operator Vyn yn - yn-1 and pn qn and wn are real numbers with pn 0 for n e -1 N - 1 wn 0 for n e 0 N - 1 and p-1 pN-1 1 A is the spectral 2 Advances in Difference Equations parameter the interval 0 N - 1 is the integral set n 01 a -n a n is a constant parameter i V Ĩ k11 k12 K k21 k22 kij e R i j 1 2 with det K 1. 1-3 The boundary condition 1.2 contains the periodic and antiperiodic boundary conditions. In fact 1.2 is the periodic boundary condition in the case where a 0 and K I the identity matrix and 1.2 is the antiperiodic condition in the case where a n and K I. We first briefly recall some relative existing results of eigenvalue problems .