International Journal of Differential Equations and Applications Volume 11 No. 3 2012, 169-181 ISSN: 1311-8080 (printed version) url: http://www.ijpam.eu P A acadpubl.eu DEATH OF THE SOLUTIONS OF SYSTEMS DIFFERENTIAL EQUATIONS WITH VARIABLE STRUCTURE AND IMPULSES K.G. Dishlieva 1 , A.B. Dishliev 2 § , S.A. Petkova 3 1 Technical University of Sofia BULGARIA 2 Department of Mathematics University of Chemical Technology and Metallurgy Sofia, BULGARIA Abstract: Nonlinear non-autonomous systems ordinary differential equations with variable structure and impulses are investigated. The changing of the system right side and impulsive effects take place simultaneously in the so called switching moments. These moments coincide with the moments when the system trajectory cancels the switching functions which are generally nonlinear. The main objective in the paper is to study the solutions which are not continuable up to infinity. The case of impulsive effects to be the cause of this phenomenon is studied. AMS Subject Classification: 34A37 Key Words: variable structure, impulses, variable impulsive moments, switch- ing functions 1. Introduction Applications of differential equations with variable structure (without impulsive effects) are primarily in the control theory: [6], [10], [13], [16], [17], [20], [25] and [28]. Impulsive equations (with fixed structure) are used most commonly for Received: April 28, 2012 c  2012 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author