Tbilisi Mathematical Journal

Measure of noncompactness and semilinear differential equations in Fréchet spaces

Amaria Arara, Mouffak Benchohra, and Fatima Mesri

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This paper deals with the existence of mild and integral solutions for a class of functional differential equations. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measure of noncompactness.

Article information

Tbilisi Math. J., Volume 12, Issue 1 (2019), 69-81.

Received: 16 October 2018
Accepted: 10 December 2018
First available in Project Euclid: 26 March 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]

semilinear differential equation semigroup theory densely defined operator nondensely defined operator mild solution integral solution fixed point


Arara, Amaria; Benchohra, Mouffak; Mesri, Fatima. Measure of noncompactness and semilinear differential equations in Fréchet spaces. Tbilisi Math. J. 12 (2019), no. 1, 69--81. doi:10.32513/tbilisi/1553565627. https://projecteuclid.org/euclid.tbilisi/1553565627

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