On positive periodic solutions of second order singular equations
On positive periodic solutions of second order singular equations
Using the fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the second order differential equations $$\begin{aligned} \textstyle\begin{cases} \ddot{x}+a(t) x=f(x),\\ x(0)=x(T),\qquad \dot{x}(0)=\dot{x}(T). \end{cases}\displaystyle \end{aligned}$$ For given nonnegative constants $0<\beta_{1}<\beta_{2}<\cdots<\beta_{N}$ , the function f may be singular at $x=\beta_{i}$ .