Strong Stability and Asymptotical Almost Periodicity of Volterra Equations in Banach Spaces

Strong Stability and Asymptotical Almost Periodicity of Volterra Equations in Banach Spaces

Almost Periodicity of Abstract Volterra Integro-differential Equations

The main purpose of this paper is to investigate almost periodic properties of various classes of (a, k)-regularized C-resolvent families in Banach spaces. We contemplate the work of many other authors working in this field, giving also some original contributions and applications. In general case, (a, k)regularized C-resolvent families under our considerations are degenerate and their subgener...

Fractional Order Semilinear Volterra Integrodifferential Equations in Banach Spaces

In this paper, sufficient conditions are established for the existence results of fractional order semilinear Volterra integrodifferential equations in Banach spaces. The results are obtained by using the theory of fractional cosine families and fractional powers of operators.

Periodic solutions for nonlinear Volterra integrodifferential equations in Banach spaces

In this paper we examine periodic integrodifferential equations in Banach spaces. When the cone is regular, we prove two existence theorems for the extremal solutions in the order interval determined by an upper and a lower solution. Both theorems use only the order structure of the problem and no compactness condition is assumed. In the last section we ask the cone to be only normal but we imp...

Semigroups and Stability of Nonautonomous Differential Equations in Banach Spaces

This paper is concerned with nonautonomous differential equations in Banach spaces. Using the theory of semigroups of linear and nonlinear operators one investigates the semigroups of weighted translation operators associated with the underlying equations. Necessary and sufficient conditions for different types of stability are given in terms of spectral properties of the translation operators ...