Electron. J. Diff. Eqns., Vol. 1997(1997), No. 24, pp. 1-20.
Lance D. Drager & William Layton
We study initial value problems for scalar, nonlinear, delay differential equations with distributed, possibly infinite, delays. We consider the initial value problem
where and are bounded and is a finite Borel measure. Motivated by the nonresonance condition for the linear case and previous work of the authors, we introduce conditions on . 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 satisfies an exponential decay condition, globally exponentially asymptotically stable.
Submitted August 14, 1997. Published December 19, 1997.
Math Subject Classification: 34K05, 34K20, 34K25
Key Words: Delay differential equation, infinite delay, initial value problem, nonresonance, asymptotic stability, exponential asymptotic stability.
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Department of Mathematics; University of Pittsburgh; Pittsburgh, PA 15260 USA.