一类非线性微分方程的可积性准则

THE INTEGRABILITY PRINCIPLE OF A KINDOF NON-LINEAR DIFFERENTIAL EQUATION

本文考虑二阶线性微分方程y″ +t2 f(t)g(y=0 ) ( 1 )的可积性 ,设G(y=∫yog(s)ds)我们证明了在一定的条件下 ,方程 ( 1 )的一切解满足估计∫∞t0G(y(t) )f(t) dt

The article mainly discusses the integrabilty of second order linear differential equation y″+t 2f(t)g(y)=0 (1), supposes G(y)=∫ y 0g(s)ds, we verify that under some condition all the solutions of equation (1) obey the estimate: ∫ ∞ t 0G(y(t))f(t)dt<+∞.