On maximal and minimal solutions for set integro-differential equations with feedback control

  • Le Thanh Quang Faculty of Mathematics and Computer Science, University of Science, Viet Nam National University - Ho Chi Minh City, Viet Nam
  • Nguyen Dinh Phu Faculty of Mathematics and Computer Science, University of Science, Viet Nam National University - Ho Chi Minh City, Viet Nam.
  • Ngo Van Hoa Division of Applied Mathematics, University of Ton Duc Thang, Viet Nam
  • Vu Ho Division of Applied Mathematics, University of Ton Duc Thang, Viet Nam

Abstract

In this paper, a class of new set-valued differential equations on semilinear Hausdorff space under classic Hukuhara derivative, called set-valued integro-differential equations (SCIDEs) which is developed under the form $D_H X\left( t \right) = F\left( {t,X\left( t \right), U(t),\int\limits_{t_0 }^t {G\left( {t,s,X\left( s \right),U(s)} \right)ds} } \right)$. Moreover, some corresponding properties of SCIDE are discussed such as existence, uniqueness, bounded of solutions. Beside that,the existence maximal and minimal solutions for SCIDE with feedback controls are presented.

Author Biography

Le Thanh Quang, Faculty of Mathematics and Computer Science, University of Science, Viet Nam National University - Ho Chi Minh City, Viet Nam
Division of Applied Mathematics
Published
2012-12-24
Section
Articles