本文研究了一类带有阻尼项的二阶半线性中立型微分方程(r(t)φ(x(t))|(x(t)+p(t)x(σ(t)))’|α-1(x(t)+p(t)x(σ((t)))’)’+φ(x(t),x′(t))+q0(t)|x(T0(t))|α-1x(T0(t))+sum from i=1 to n(qi(t)|x(Ti(t))|βi-1x(Ti(t))=0)的解的性质,其中n是一个偶数,利用一些新的技巧,我们获得了方程解的振动的一些充分条件,并且给出例子阐述我们所得的结论.
摘要(英文):
A class of second-order quasilinear neutral differential equation with damped (r(t)Ф(x(t))|(x(t)+p(t)x(σ(t)))′|^α-1(x(t)+p(t)x(σ(t)))′)′+φ(x(t),x′(t))+q0(t)x(τ0(t))|^α-1x(τ0(t))+∑i=1^n(t)x(τi(t))|^βi-1x(τi(t))=0 be investigated in this paper, where n is an even number. Using a new method, we obtain some sufficient conditions for the oscillation of the above equation. Example be inserted to illustrate this results.