一类二阶非线性泛函微分方程解的振动性

Oscillatory behavior of solutions of certain second order nonlinear differential equation

讨论了一类二阶非线性泛函微分方程(a(t)y(′t)σ)′+q(t)f(y(τ(t)))g(y(′t))=0,t≥t0,σ是分母为奇数的正有理分数时方程解的振动性,得到此类方程的解振动的充分性判据,改进并推广了已有文献中的相应结论.

Oscillatory behavior of solutions to the second order nonlinear functional ditterential equation （α（t）y＇（t）σ）＇＋q（t）f（y）τ（t）））g（y＇（t））=0,t≥t0 was discussed, of which σ is a positive quotient of integer over odd integers, and some new sufficient conditions were established for the oscillatory, which extended and improved the corresponding results in many known literatures.