Kuratowski measure of noncompactness and integro-differential equations in Banach spaces

Volume 14, Issue 2, pp 109--117 http://dx.doi.org/10.22436/jnsa.014.02.06

Publication Date: September 04, 2020 Submission Date: June 03, 2020 Revision Date: June 20, 2020 Accteptance Date: July 21, 2020

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Authors

Mariam B Traore - Des Techniques et des Technologies de Bamako, Ecole Doctorale des Sciences et Technologies du Mali, Universite des Sciences, B.P. E2528, Bamako, Mali. Ouateni Diallo - Des Techniques et des Technologies de Bamako, Ecole Doctorale des Sciences et Technologies du Mali, Universite des Sciences, B.P. E2528, Bamako, Mali. Mamadou Abdoul Diop - Departement de Mathematiques, Universite Gaston Berger de Saint-Louis, UFR SAT, B.P. 234, Saint-Louis, Senegal.

Abstract

This paper focuses on the existence of mild solutions in Banach space for a first order semi-linear integro-differential equation. The results are achieved with the fixed-point theorem and Kuratowski measure of noncompactness. We conclude this study with an example to illustrate our findings.

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Keywords

• Integro-differential equation
• mild solution
• fixed point
• Kuratowski measure of noncompactness
• resolvent operator

MSC

•  34G20
•  37L05
•  47J35
•  65J08

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