【摘要】 在α≠1且β∈(0,1)情形下研究了一阶具非线性中立项时滞微分方程[x(t)-pxα(t-τ)]′+q(t)xβ(t-σ),t≥t0解的振动性和非振动性,在β∈(0,1)情形下获得了上述方程所有有界解振动的充要条件,同时在α∈(1,∞)且β∈(0,1)情形下获得了上述方程存在无界正解的充分条件.这些新的结果填补了已有文献中空白.更多还原

【Abstract】 The oscillatory behavior of solutions of the delay differential equations with nonlinear neutral term[x（t）-px^α（t-τ）]′+q（t）x^β（t-σ）,t≥t₀is studied in the case when α≠1 and β∈（0,1）.The necessary and sufficient conditions are obtained which guarantee every bounded solutions of the above equation oscillates in the case β∈（0,1）,and the sufficient conditions are also obtained for the existence of an unbounded positive solution of the above equation in the case α∈（1,∞） and β∈（0,1）.These results fill a gap in the literature.更多还原