Ravi Agarwal, Snezhana Hristova, Donal O'Regan
Abstract:
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 |
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Snezhana Hristova Plovdiv University Tzar Asen 24 4000 Plovdiv, Bulgaria email: snehri@gmail.bg |
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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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