Perron's theorem for nondensely defined partial functional differential equations

Abstract

The aim of this work is to establish a Perron type theorem for some nondensely defined partial functional differential equations with infinite delay. More specifically, we show that if the nonlinear delayed part is "small" (in a sense to be made precise below), then the asymptotic behavior of solutions can be described in terms of the dynamic of the unperturbed linear part of the equation.

Keywords

• unctional differential equations
• asymptotic behavior
• perron's theorem