Electron. J. Diff. Equ., Vol. 2015 (2015), No. 49, pp. 1-19.

Stability with respect to initial time difference for generalized delay differential equations

Ravi Agarwal, Snezhana Hristova, Donal O'Regan

Stability with initial data difference for nonlinear delay differential equations is introduced. This type of stability generalizes the known concept of stability in the literature. It gives us the opportunity to compare the behavior of two nonzero solutions when both initial values and initial intervals are different. Several sufficient conditions for stability and for asymptotic stability with initial time difference are obtained. Lyapunov functions as well as comparison results for scalar ordinary differential equations are employed. Several examples are given to illustrate the theory.

Submitted October 20, 2014. Published February 19, 2015.
Math Subject Classifications: 34K45, 34D20.
Key Words: Stability; initial data difference; Lyapunov function; delay differential equation.

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Ravi Agarwal
Department of Mathematics
Texas A&M University-Kingsville
Kingsville, TX 78363, USA
email: agarwal@tamuk.edu
Snezhana Hristova
Plovdiv University
Tzar Asen 24
4000 Plovdiv, Bulgaria
email: snehri@gmail.bg
Donal O'Regan
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
Galway, Ireland
email: donal.oregan@nuigalway.ie

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