具有时滞的非线性强迫微分方程振动的充分必要条件(英文)

对于一类特殊的具有时滞的二阶次线性强迫微分方程 x″( t) + a( t) | x(τ( t) ) | γsgnx(τ( t) ) =g( t) ( 0 <γ<1 ) 。

带阻尼的非线性强迫分数阶微分方程的区间振动准则

考虑一类带阻尼的非线性强迫分数阶微分方程的解的振动性D_tα[r（t）ψ（x（t））D_tαx（t）]＋p（t）ψ（x（t））D_tαx（t）＋q（t）f（x（t））=e（t）,t≥t_0〉0,0〈α〈1,其中Dαt（·）定义为关于变量t的修正黎曼-刘维尔导数.通过运用一个广义黎卡提变换,不等式和积分平均技巧,该文建立了此方程的一些新的振动准则.

OSCILLATION OF A FORCED SECOND ORDER NONLINEAR EQUATION

This paper gives several criteria on the oscillatory behavior of solutions of the forced secondorder equation x″+ a(t)i(x) = g(t), where g(t) is oscillatory) by using a geometric idea. Asspecial cases these results include and improve some recent results, given by J. S. Wong. Thecriteria also solve the problem posed by H. Onose in Mathematical Reviews, 1986.