TAILIEUCHUNG - Báo cáo sinh học: "Research Article Positive Decreasing Solutions of Higher-Order Nonlinear Difference Equations"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Positive Decreasing Solutions of Higher-Order Nonlinear Difference Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 973432 16 pages doi 2010 973432 Research Article Positive Decreasing Solutions of Higher-Order Nonlinear Difference Equations B. Krasznai I. Gyori and M. Pituk Department of Mathematics University of Pannonia . Box 158 8201 Veszprem Hungary Correspondence should be addressed to M. Pituk pitukm@ Received 23 December 2009 Accepted 13 May 2010 Academic Editor Agacik Zafer Copyright 2010 B. Krasznai 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. It is shown that the decay rates of the positive monotone decreasing solutions approaching the zero equilibrium of higher-order nonlinear difference equations are related to the positive characteristic values of the corresponding linearized equation. If the nonlinearity is sufficiently smooth this result yields an asymptotic formula for the positive monotone decreasing solutions. 1. Introduction and the Main Results Let R C and Z be the set of real and complex numbers and the set of integers respectively. The symbol Z denotes the set of nonnegative integers. Recently Aprahamian et al. 1 have studied the second-order nonlinear difference equation A2x n - 1 cAx n f x nf 0 n e Z where c 0 Ax n x n 1 - x n so that A2x n - 1 x n 1 - 2x n x n - 1 and f R R is a Lipschitz continuous function such that f 0 in 0 1 and f 0 is identically in -TO 0 u 1 to . As noted in 1 is related to the discretization of traveling wave solutions of the Fisher-Kolmogorov partial differential equation. The main result of 1 is the following theorem about the existence of positive decreasing solutions of see 1 Theorem and its proof . 2 Advances in Difference Equations Theorem . In addition to the above hypotheses on f suppose that there exist e e 0 1 and k 0 such

• 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