Existence and compactness of solution of semilinear integro-differential equations with finite delay

  • F. Sahraoui Laboratory Math., Sidi-Bel-Abbe`s Univ., Algeria
  • А. Ouahab Laboratory Math., Sidi-Bel-Abbe`s Univ., Algeria
Keywords: Mild solutions, resolvent operator, Banach fixed point, measure of non-compactness, attractivity.

Abstract

UDC 517.9

We present some existence and uniqueness results for a class of functional integro-differential evolution equations  generated by the resolvent operator for which the semigroup is not necessarily compact. It  is proved that the set of solutions is compact.  Our approach is based on fixed point theory.  Finally, some examples are given to illustrate the results.

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Published
08.11.2022
How to Cite
SahraouiF., and OuahabА. “Existence and Compactness of Solution of Semilinear Integro-Differential Equations With Finite Delay”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 9, Nov. 2022, pp. 1231 -55, doi:10.37863/umzh.v74i9.7106.
Section
Research articles