Dynamic equation on time scale with almost periodic coefficients

Abstract

In this paper, we discuss a nonautonomous dynamical equation on time scale in a Banach space. The nonautonomous case is particularly important and needs to be studied because it is frequently met in the mathematical models of evolutionary processes. We give sufficient condition for equation to have an exponentially stable almost periodic solution in terms of the accretiveness of an operator. At the end, examples are given to illustrate the analytical findings.

Keywords

• time scale
• nonlinear equations
• evolution semigroup
• accretive operator
• almost periodic function
• 47d06
• 42a75
• 34n05