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Making the numerical abscissa negative for a class of neutral equations

Pages: 256 - 262, Issue Special, July 2003

 Abstract        Full Text (160.9K)              

R.H. Fabiano - Department of Mathematical Sciences, University of North Carolina at Greensboro, 340 Bryan Building, Greensboro, NC 27410, United States (email)
J. Turi - Programs in Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083-0688, United States (email)

Abstract: We consider the question of exponential stability of the solution semi- group for a class of scalar differential-difference equations of neutral type. Under very weak assumptions on the coefficients in the equation we show how to construct an appropriate inner product on the underlying state space, which guarantees that the numerical abscissa of the infinitesimal generator is negative.

Keywords:  delay equation, numerical abscissa.
Mathematics Subject Classification:  45L10, 34k20, 34k30.

Received: September 2002;      Revised: March 2003;      Published: April 2003.