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Báo cáo nghiên cứu khoa học: " EXISTENCE OF SOLUTIONS OF SET CONTROL DIFFERENTIAL EQUATIONS"

Gần đây, lĩnh vực phương trình vi phân đã được nghiên cứu trong một phương pháp rất trừu tượng.Thay vì xem xét hành vi của một trong những giải pháp của một phương trình vi phân, một trong những nghiên cứu bó giải pháp của nó (xem [8]). | TẠP CHÍ PHÁT TRIỂN KH CN TẬP 10 SÓ 06 - 2007 EXISTENCE OF SOLUTIONS OF SET CONTROL DIFFERENTIAL EQUATIONS Nguyen Dinh Phu Tran Thanh Tung University of Natural Sciences VNU-HCM Manuscript received on June 06th 2006 Manuscript received on May 11th 2007 ABSTRACT Recently the field of differential equations has been studying in a very abstract method. Instead of considering the behaviour of one solution of a differential equation one studies its sheaf-solution see 8 . Instead of studying a differential equation one studies differential inclusion see 10 . Specially one studies set differential equation a differential equation whose variables and derivative are sets see 1-7 a fuzzy differential equation is generalized to be fuzzy control differential equation FCDE see 13 . In this paper a set differential equation is generalized to be set control differential equation SCDE and we present the existence and comparison of solutions of SCDE .This paper is a continuation of our works in this direction see 11-15 . Keywords Differential equations Set differential equations Set control differential equations. 1. INTRODUCTION In 1-8 authors studied the existence and comparison of solutions of the set differential equation SDE DhX I F t X t where X t0 X 0 e Kc Rn X t e K Rn t e tữ T I c R and F I X Kc Rn Kc Rn . In this paper we give the so-called set control differential equation SCDE in the form DhX I F t X t U t whereX t0 X0 e Kc Rn X t e K Rn U t e Kc Rp t e t0 T I c R F I X Kc Rn X K Rp Kc Rn and study existence of solutions and comparison solutions of SCDE. The paper is organized as follows we recall some basic concepts and notations which are useful in next sections in section 2 and some results on SDE in section 3. Existence results on solutions and comparison of solutions of SCDE are presented in section 4. 2. PRELIMINARIES We recall some notations and concepts presented in detail in recent series works of V. Lakshmikantham et al. See 1-8 . Trang 5 Science Technology .