tailieunhanh - báo cáo hóa học: " Nonlocal conditions for differential inclusions in the space of functions of bounded variations"

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: Nonlocal conditions for differential inclusions in the space of functions of bounded variations | Agarwal and Boucherif Advances in Difference Equations 2011 2011 17 http content 2011 1 17 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Nonlocal conditions for differential inclusions in the space of functions of bounded variations Ravi Agarwal1 2 and Abdelkader Boucherif2 1 Correspondence aboucher@ 2Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Box 5046 Dhahran 31261 Saudi Arabia Full list of author information is available at the end of the article SpringerOpen0 Abstract We discuss the existence of solutions of an abstract differential inclusion with a right-hand side of bounded variation and subject to a nonlocal initial condition of integral type. AMS Subject Classification 34A60 34G20 26A45 54C65 28B20 Keywords Set-valued maps of bounded variation Differential inclusion Nonlocal initial condition Generalized Helly selection principle Fixed point of multivalued operators 1 Introduction Solutions of differential equations with smooth enough coefficients cannot have jump discontinuities see for instance 1 2 . The situation is quite different for systems described by differential equations with discontinuous right-hand sides 3 . Examples of such systems are mechanical systems subjected to dry or Coulomb frictions 4 optimal control problems where the control parameters are discontinuous functions of the state 5 impulsive differential equations 6 measure differential equations pulse frequency modulation systems or models for biological neural nets 7 . For these systems the state variables undergo sudden changes at their points of discontinuity. The mathematical models of many of these systems are described by multivalued differential equations or differential inclusions 8 . Let X be a Banach space with norm - X. Then X is a metric space with the distance dX defined by dx x y x y X for any x y e X. Let I 0 T be a compact real interval. We are