# American Institute of Mathematical Sciences

2003, 2003(Special): 256-262. doi: 10.3934/proc.2003.2003.256

## Making the numerical abscissa negative for a class of neutral equations

 1 Department of Mathematical Sciences, University of North Carolina at Greensboro, 340 Bryan Building, Greensboro, NC 27410, United States 2 Programs in Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083-0688, United States

Received  September 2002 Revised  March 2003 Published  April 2003

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.
Citation: R.H. Fabiano, J. Turi. Making the numerical abscissa negative for a class of neutral equations. Conference Publications, 2003, 2003 (Special) : 256-262. doi: 10.3934/proc.2003.2003.256
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