## African Diaspora Journal of Mathematics

### A First-Order Periodic Differential Equation at Resonance

Eric R. Kaufmann

#### Abstract

We consider the existence of a periodic solution to the first-order nonlinear problem

\begin{eqnarray*} &&x'(t) = -a(t)x(t)+ q ( t, x(t) ),\; \mbox{ a.e. on } (0, T),\\ &&x(0) = x(T), \end{eqnarray*}

where the nonlinear term $q$ is Carathéodory with respect to $L^1[0, T]$. The coefficient function $a$ is such that the differential equation is non-invertible. The technique used to establish our existence result is Mahwin's coincidence degree theory.

#### Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 11, Number 1 (2011), 66-74.

Dates
First available in Project Euclid: 21 April 2011

Permanent link to this document

Mathematical Reviews number (MathSciNet)
MR2792211

Zentralblatt MATH identifier
1244.34025

Subjects
Primary: 40
Secondary: 46 46

#### Citation

Kaufmann , Eric R. A First-Order Periodic Differential Equation at Resonance. Afr. Diaspora J. Math. (N.S.) 11 (2011), no. 1, 66--74. https://projecteuclid.org/euclid.adjm/1303391946