Topological Methods in Nonlinear Analysis

A local existence theorem for a class of delay differential equations

Ioan I. Vrabie

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Abstract

The goal of this paper is to show that some classes of partial differential functional equations admit a natural formulation as ordinary functional differential equations in infinite dimensional Banach spaces. Moreover, the equations thus obtained are driven by continuous right-hand sides satisfying the compactness assumptions required by the infinite-dimensional version of a Peano-like existence theorem. Two applications, one to a semilinear wave equation with delay and another one to a pseudoparabolic PDE in Mechanics, are included.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 597-612.

Dates
First available in Project Euclid: 21 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1482289231

Digital Object Identifier
doi:10.12775/TMNA.2016.023

Mathematical Reviews number (MathSciNet)
MR3642775

Zentralblatt MATH identifier
1365.34134

Citation

Vrabie, Ioan I. A local existence theorem for a class of delay differential equations. Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 597--612. doi:10.12775/TMNA.2016.023. https://projecteuclid.org/euclid.tmna/1482289231


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