二阶非线性中立型时标动态方程非振动解的存在性

Existence of Nonoscillatory Solutions to Second-order Nonlinear Neutral Dynamic Equations on Time Scales

利用Krasnoselskii不动点定理,建立了研究二阶非线性中立型时标动态方程[r(t)(x(t)+p(t)x(t-τ))Δ]Δ+∑mi=1Qi(t)fi(x(t-σi))=0,t∈T的非振动解的存在性条件。所得结果包含二阶非线性中立型微分方程相应的结论,并给出二阶非线性中立型差分方程新的判别准则。

By employing Krasnoselskii＇s fixed pomt theorem, the existence of nonoscillatory solutions of the second-order nonlinear neutral dynamic equations on time scales [r（t）（x（t）＋p（t）x（t-τ））^△]^△＋^m∑i=1Qi（t）fi（x（t-σi））=0,t∈T is established. The obtained results cover those for second-order nonlinear neutral differential equations and provide new crtteria for second-order nonlinear neutral differential equations.