## African Diaspora Journal of Mathematics

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

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

#### 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**

https://projecteuclid.org/euclid.adjm/1303391946

**Mathematical Reviews number (MathSciNet)**

MR2792211

**Zentralblatt MATH identifier**

1244.34025

**Subjects**

Primary: 40

Secondary: 46 46

**Keywords**

Coincidence theory Brower degree nonlinear dynamic equation periodic resonance

#### 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