Almost periodicity of abstract Volterra integro-differential equations

Abstract

© 2016 by the Tusi Mathematical Research Group. 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 subgenerators are multivalued linear operators or pairs of closed linear operators. We also consider the class of (a, k)-regularized (C 1 , C 2 )-existence and uniqueness families, where the operators C 1 and C 2 are not necessarily injective, and provide several illustrative examples of abstract Volterra integrodifferential equations which do have almost periodic solutions.