二阶泛函微分方程的渐近性和振动性

Oscillatory and Asymptotic Criteria for Second Order Functional Differential Equations

摘要: 研究了二阶非线性中立型时滞泛函微分方程A(t)x(t)-∑li=1Pi(t)x(t-τ)"+∑mj=1Qj(t)fj(x(t-σj))=0的振动性,分别得到了方程所有解振动和方程存在非振动解的充分条件,推广和改进了现有文献中的相关结果.

Abstract: The oscillation of the second order nonlinear neutral delay functional differential equation A(t)x(t)-∑li=1Pi(t)x(t-τ)"+∑mj=1Qj(t)fj(x(t-σ))=0 is established.Sufficient conditions for oscillation of all solutions of the equation and existence of nonoscillatory solution are obtained respectively,which extend and improve the corresponding results of literature.