Advances in Operator Theory

Almost periodicity of abstract Volterra integro-differential equations

Marko Kostić

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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 integro-differential equations which do have almost periodic solutions.

Article information

Adv. Oper. Theory, Volume 2, Number 3 (2017), 353-382.

Received: 11 January 2017
Accepted: 2 June 2017
First available in Project Euclid: 4 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B15: Almost and pseudo-almost periodic solutions
Secondary: 47D06, 47D62, 34G25

abstract Volterra integro-differential equations $(a, k)$-regularized $C$-resolvent families multivalued linear operators degenerate integro-differential equations almost periodicity


Kostić, Marko. Almost periodicity of abstract Volterra integro-differential equations. Adv. Oper. Theory 2 (2017), no. 3, 353--382. doi:10.22034/aot.1701-1096.

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