Necessary and sufficient conditions for stability of Volterra integro-dynamic equation on time scales

Youssef N. Raffoul

Address: Department of Mathematics, University of Dayton, Dayton, OH 45469-2316


Abstract: In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.

AMSclassification: primary 45D05; secondary 34N05, 34D05, 39A12.

Keywords: necessary, sufficient, time scales, Lyapunov functionals, stability, zero solution.

DOI: 10.5817/AM2016-1-21