Periodic solutions of almost linear Volterra integro-dynamic systems

Dynamic Behaviors of an Almost Periodic Volterra Integro Dynamic Equation on Time Scales

This paper is concerned with an almost periodic Volterra integro dynamic equation on time scales. Based on the theory of calculus on time scales, by using differential inequality theory and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the global attractivity of the system are obtained. Then, by using the properties of almost periodic func...

Bounded Solutions of Almost Linear Volterra Equations

Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. AMS Subject Classifications: 45D05, 45J05.

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

Stability properties and existence theorems of pseudo almost periodic solutions of linear Volterra difference equations

Correspondence: [email protected]. ac.jp Department of Information Science, Okayama University of Science, 1-1 Ridai-chyo, Kitaku, Okayama 700-0005, Japan Abstract The purpose of this article is to discuss the existence of pseudo almost periodic solutions of linear Volterra equation: x(n + 1) = A(n)x(n) + ∑n s=−∞ F(n, s)x(s) + p(n) , n Î Z, by using an exponentially stable of the zero solution, wh...

Characterizations of Positive Linear Volterra Integro-differential Systems

We first give a criterion for positivity of the solution semigroup of linear Volterra integro-differential systems. Then, we offer some explicit conditions under which the solution of a positive linear Volterra system is exponentially stable or (robustly) lies in L2[0,+∞). Mathematics Subject Classification (2000). Primary 34A30; Secondary 34K20.