一类二阶非线性微分方程的振动性

Oscillation for a class of second order nonlinear differential equations

利用一个基本不等式 ,研究了一类既非超线性又非次线性的二阶微分方程 x″( t) +a( t) | x( t) | βsgn x( t) + b( t) | x( t) | γsgn x( t) =0的振动性 ,其中 a( t) ,b( t)允许变号 ,0 <β<1 ,γ>1 .

By using a basic inequality,the oscillation of a class of second order nonlinear differential equations x″(t)+a(t)|x(t)| βsgnx(t)+b(t)|x(t)| γsgnx(t)=0 is studied,which is neither super linear nor sub linear,where t∈[t 0,∞),a(t),b(t)∈C[t 0,∞) are allowed to change signs,and 0<β<1,γ>1.