【摘要】 考虑如下具有正负系数的中立型时滞微分方程:[a(t)x(t)-b(t)x(t-r)]′+p(t)x(t-τ)-q(t)x(t-δ)=0,t≥t1>0,其中a(t)∈C([t,∞),(0,∞));p(t),q(t)∈C([t1,∞),R+),R+=[0,∞) 本文通过在Banach空间中,用勒贝格控制收敛定理和分析学中的一些技巧建立了该方程存在最终正解的一个充分条件,并举例加以说明 当a(t)≡1时,已有许多文章讨论过对上述方程通过换元化为a(t)≡1的情形,但通过本文可以看出,对上述方程的进一步研究是有意义的更多还原

【Abstract】 In this paper, we obtain the sufficient conditions, by Lebesgue’s dominated convergence theorem in the Banach space and some skills in analytics, for existence positive solutions of a class of neutral delay differential equations with positive and negative coefficients as follow:′+p(t)x(t-τ)-q(t)x(t-δ)=0,t≥t1>0, where, a(t)∈C(me examples. When , there are many papers talking about it, however, we can transfer above equation into the form of , but we can see that farther research of above equation is significative by this paper.更多还原