Báo cáo hoa học: "Research Article Nonlocal Controllability for the Semilinear Fuzzy Integrodifferential Equations in n-Dimensional Fuzzy Vector Space"

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 Nonlocal Controllability for the Semilinear Fuzzy Integrodifferential Equations in n-Dimensional Fuzzy Vector Space | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 734090 16 pages doi 2009 734090 Research Article Nonlocal Controllability for the Semilinear Fuzzy Integrodifferential Equations in n-Dimensional Fuzzy Vector Space Young Chel Kwun 1 Jeong Soon Kim 1 Min Ji Park 1 and Jin Han Park2 1 Department of Mathematics Dong-A University Pusan 604-714 South Korea 2 Division of Mathematics Sciences Pukyong National University Pusan 608-737 South Korea Correspondence should be addressed to Jin Han Park jihpark@ Received 23 February 2009 Revised 20 June 2009 Accepted 3 August 2009 Recommended by Tocka Diagana We study the existence and uniqueness of solutions and controllability for the semilinear fuzzy integrodifferential equations in n-dimensional fuzzy vector space En n by using Banach fixed point theorem that is an extension of the result of J. H. Park et al. to n-dimensional fuzzy vector space. Copyright 2009 Young Chel Kwun 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 Many authors have studied several concepts of fuzzy systems. Diamond and Kloeden 1 proved the fuzzy optimal control for the following system X t a f x f u t x 0 x0 where x - and u - are nonempty compact interval-valued functions on E1. Kwun and Park 2 proved the existence of fuzzy optimal control for the nonlinear fuzzy differential system with nonlocal initial condition in EN by using Kuhn-Tucker theorems. Fuzzy integrodifferential equations are a field of interest due to their applicability to the analysis of phenomena with memory where imprecision is inherent. Balasubramaniam and Muralisankar 3 proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. They considered the semilinear

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