Periodic solutions for a nonautonomous ordinary differential equation
暂无分享,去创建一个
We consider the nonautonomous differential equation of second order x″+a(t)x−b(t)x2+c(t)x3=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 positive T-periodic solutions for this equation, using coincidence degree theories.
[1] Paul H. Rabinowitz,et al. Free vibrations for a semilinear wave equation , 2010 .
[2] A note on periodic solutions of some nonautonomous differential equations , 1986, Bulletin of the Australian Mathematical Society.
[3] E. A. Silva. Linking theorems and applications to semilinear elliptic problems at resonance , 1991 .
[4] G. Austin,et al. Biomathematical model of aneurysm of the circle of willis, i: the duffing equation and some approximate solutions , 1971 .