Bifurcation on the oscillation of a class of second order ordinary differential equations

摘要

This paper discusses the bifurcation on the oscillation of the following second order ordinary differential equation:x″(t)+tλp(t)f(x)=0.Several conditions for the functions p(t), f(x) are obtained, under which the equation is nonoscillatory as λ<−1, and oscillatory as λ>−1, that is, λ=−1 is a bifurcation value on oscillation of the equation.