Oscillation of first order neutral nonlinear differential equations with variable coefficients

作者：Li WT

来源：Indian Journal of Pure and Applied Mathematics, 1998, 29(6): 605-615.

• neutral nonlinear equation
• oscillation
• comparison theorem

The first order neutral nonlinear differential equation with variable coefficients is considered
d/dt (x(t) - R(t)x(t-r)) + P(t) Pi(i=1)(m) \x(t-tau(i))\(alpha i) sgnx (t-tau(i))=0,
where P, R is an element of C([t(0), infinity), R+), r is an element of (0, infinity) and tau(1), tau(2), ...., tau(m) are nonnegative numbers. We will establish a necessary and sufficient condition for the oscillation of all solutions. This will lead to several new criteria for the oscillation of the above equation without the restriction
(t0)integral(infinity) P(s)ds = infinity or (t0)integral(infinity)sP(s) integral(s)(infinity) P(u)duds = infinity,
commonly used in the literature.

• 出版日期1998-6
• 单位兰州理工大学