具有多变时滞中立型微分方程的振动性

Oscillations of neutral differential equations withmany and variable time delays

考虑具有多变时滞中立型微分方程x(t)-∑li=1pi(t)x(t-τi(t))′+∑mj=1qj(t)x(t-σj(t))=0,获得了该方程所有解振动的几族充分条件.其中定理3的条件是"Sharp"条件,即当pi(t),τi(t),qj(t),σj(t)(i=1,2,…,l,j=1,2,…,m)为常数时,条件是充分必要的.

The following neutral differential equation with many and variable time delays is considered:~′+∑mj=1q_j(t)x(t-σ_j(t))=0.Several classes of sufficient conditions are obtained for the oscillation of all of its solutions.Conditions of Theorem 3 are 'sharp' in the sense that whenp_i(t),τ_i(t),q_j(t),σ_j(t)(i=1,2,...,l,j=1,2,...,m) are constants, the conditions are also sufficient and necessary.