一类三阶拟线性微分方程非振动解的渐近性

主要讨论的是一类三阶拟线性微分方程(p(t)|u″|~(α-1)u″)′+q(t)|u|~(β-1)u=0其中α0,β0,p(t)和q(t)是定义在区间a,∞)上的连续函数,且满足当t≥a时p(t)0,q(t)0.当t→∞时此方程满足∫_a~∞1/((p(t))~(1/α))dt=∞的特殊非振动解存在的充分必要条件.

The Existence of Nonoscillatory Soluation of one Type Third-order Quasilinear Differential Equation

This paper is concerned with nonoscillatory solutions of the third order quasi-lineardifferential equation(p(t)|u"|~(α-1)u")' + q(t)|u|~(β-1)u=0whereα>0,β>0,p(t) and q(t) are continuous functions on an infinite intervalα,∞) satisfyingp(t)>0 and q(t)>0,t≥α.Give the necessary and sufficient conditions that equationhas specific nonoscillatory solutions when t→∞the equation satisfies∫_α~∞1/((p(t))~(1/α)) dt =∞.