Dynamics of Partial Differential Equations

Volume 15 (2018)

Number 1

A class of semilinear delay differential equations with nonlocal initial conditions

Pages: 45 – 60

DOI: https://dx.doi.org/10.4310/DPDE.2018.v15.n1.a2

Author

Ioan I. Vrabie (Mathematics Institute of the Romanian Academy, Iaşi, Romania)

Abstract

The goal of this paper is to prove an existence result for a class of semilinear delay functional differential equation subjected to nonlocal initial conditions. As applications an existence theorem referring to periodic solutions to a semilinear wave partial differential functional equation is included.

Keywords

delay semilinear differential equations, nonlocal initial conditions, local existence, metric fixed point arguments, topological fixed point arguments, $T$-periodic semilinear wave equation

2010 Mathematics Subject Classification

Primary 34K13, 34K30. Secondary 35L05, 35R10, 47E99.

Received 8 May 2017

Published 14 December 2017