Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
837847 | Nonlinear Analysis: Real World Applications | 2011 | 6 Pages |
Abstract
A nonautonomous system of ordinary differential equations dx/dt=X(t,x),x=(y,z) admitting the invariant set y=0y=0 is considered. It is assumed that there exists a nonnegative Lyapunov function V(t,x)V(t,x) whose derivative is nonpositive. It is assumed that all solutions x(t)=(y(t),z(t))x(t)=(y(t),z(t)) of this system lying on the integral set V(t,x)=0V(t,x)=0, have the property limt→∞‖y(t)‖=0limt→∞‖y(t)‖=0. The theorem on the uniform stability of the set y=0y=0 is proved.
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Authors
Alexander O. Ignatyev, Oleksiy A. Ignatyev,