In this paper a method for studying stability of the equation not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation is not exponentially stable, the delay equation can be exponentially stable.
In this paper we demonstrate that in many cases the investigation of the problem of controlling chaos, which is of great theoretical and practical importance, can be reduced to the stability analysis of the corresponding integro-differential equations. We consider stabilization for the configuration of a magneto-elastic beam and a two magnet system known as "Moon's beam". Then we study an unstable system, in which the Lorenz attractor appears, and stabilize it by a control in integral form. In order to obtain stability results, we propose a special technique which is based on the idea of reduction of integrodifferential equations to systems of ordinary differential equations.
Theorems on the unique solvability and nonnegativity of solutions to the characteristic initial value problemu1,1(t,x)=l0(u)(t,x)+l1(u1,0)(t,x)+l2(u0,1)(t,x)+q(t,x), u(t,c)=α(t)fort∈[a,b], u(a,x)=β(x) for x∈[c,d]given on the rectangle[a,b]×[c,d]are established, where the linear operatorsl0,l1,l2map suitable function spaces into the space of essentially bounded functions. General results are applied to the hyperbolic equations with essentially bounded coefficients and argument deviations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.