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báo cáo hóa học:" Research Article On an Exponential-Type Fuzzy Difference Equation"

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 On an Exponential-Type Fuzzy Difference Equation | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 196920 19 pages doi 10.1155 2010 196920 Research Article On an Exponential-Type Fuzzy Difference Equation G. Stefanidou G. Papaschinopoulos and C. J. Schinas School of Engineering Democritus University of Thrace 67100 Xanthi Greece Correspondence should be addressed to G. Papaschinopoulos gpapas@env.duth.gr Received 11 March 2010 Revised 10 June 2010 Accepted 24 October 2010 Academic Editor Roderick Melnik Copyright 2010 G. Stefanidou 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. Our goal is to investigate the existence of the positive solutions the existence of a nonnegative equilibrium and the convergence of a positive solution to a nonnegative equilibrium of the fuzzy difference equation xn 1 1 - p-Q xn-j 1 - e A x k e 2 3 . n 0 1 . where A and the initial values x_k 1 x-k 2 . x0 belong in a class of fuzzy numbers. 1. Introduction Fuzzy difference equations are approached by many authors from a different view. In 1 the authors developed the stability results for the fuzzy difference equation Mn 1 f n Hn Un0 uo 1.1 in terms of the stability of the trivial solution of the ordinary difference equation Zn 1 g n Zn Zn0 Zo 1.2 where f n u is continuous in u for each n and un f e En for each n n0 where En u Rn 0 1 such that u satisfies the following i u is normal ii u is fuzzy convex iii u is upper semicontinuous iv u 0 x e Rn u x 0 is compact and g n r is a continuous and nondecreasing function in r for each n. 2 Advances in Difference Equations In 2 the authors studied the second-order linear constant coefficient fuzzy difference equation of the form y k 2 ay k 1 by k g k 11 12 . 1-m 1.3 for k 0 1 2 . where y k is the unknown function of k and a b are real constants with b Ỷ 0. g k 11 12 . 1m is a known function