Multiple Periodic solutions and Positive Homoclinic Solution for a differential equation

Abstract

We consider the nonautonomous differential equation of second order $x''- a(t)x+b(t) x^2+c(t)x^{3}=0$, where $a(t),b(t),c(t)$ are $T$-periodic functions. This is a biomathematical model of an aneurysm in the circle of Willis. We prove the existence of at least two $T$-periodic solution for this equation, using coincidence degree theories.