IJPAM: Volume 57, No. 3 (2009)
FUNCTIONS FOR DIFFERENTIAL EQUATIONS
Department of Applied Mathematics and Modeling
Plovdiv, 4000, BULGARIA
e-mail: [email protected]
Abstract.A special type of practical stability for differential equations with ``maxima'' is introduced. The definitions are based on the application of two different measures as well as on the application of a scalar product on a cone. This allows us to use cone valued Lyapunov functions for investigation of stability properties of the solutions. Some sufficient conditions for d-practical stability in terms of two measures of nonlinear differential equations with ``maxima'' are obtained. An example illustrates the practical application of the proved results.
Received: March 19, 2008
AMS Subject Classification: 34D20
Key Words and Phrases: practical stability, two measures, cone valued Lyapunov functions, differential equations with ``maxima''
Source: International Journal of Pure and Applied Mathematics