Abstract
We study initial value problems for scalar, nonlinear, delay differential equations with distributed, possibly infinite, delays. We consider the initial value problem (Equation presented), where ψ and f are bounded and μ is a finite Borel measure. Motivated by the nonresonance condition for the linear case and previous work of the authors, we introduce conditions on g. Under these conditions, we prove an existence and uniqueness theorem. We show that under the same conditions, the solutions are globally asymptotically stable and, if μ satisfies an exponential decay condition, globally exponentially asymptotically stable.
Original language | English |
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Pages (from-to) | 1-20 |
Number of pages | 20 |
Journal | Electronic Journal of Differential Equations |
Volume | 1997 |
State | Published - Dec 19 1997 |
Keywords
- Asymptotic stability
- Delay differential equation
- Exponential asymptotic stability
- Infinite delay
- Initial value problem
- Nonresonance