# Existence and positivity of solutions for a nonlinear periodic differential equation

## Ernest Yankson

Address: Department of Mathematics and Statistics, University of Cape Coast, Ghana

E-mail: ernestoyank@yahoo.com

Abstract: We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.

AMSclassification: primary 34A37; secondary 34A12, 39A05.

Keywords: fixed point, large contraction, periodic solution, positive solution.

DOI: 10.5817/AM2012-4-261