Positive periodic solutions of nonlinear differential equations

The nonlinear differential equation *\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x'\left( t \right) = - \delta \left( t \right)x\left( t \right) + f\left( {t,x\left( t \right)} \right)$$ \end{document} is considered, where δ(t) is a periodic function of periodic T, f(t,x) is continuous and periodic in t. It is showed that (*) has at least two positive T-periodic solutions under certain growth conditions imposed on f. Applications will be presented to illustrate the main results.