Oscillation of solutions of second-order neutral delay differential equations with integrable coefficients
The equation considered is \[ \bigl(a(t)[x(t)+p(t)x(t-\tau)]'\bigr)'+ q(t)f[x(t-\sigma)]=0,\;t\geq t_0,\tag{1} \] where \(\tau,\sigma>0\), \(a,p,q\in C([t_0,\infty),{\mathbb{R}})\), \(0\leq p(t)\leq 1\), \(q(t)\geq 0\), \(a(t)>0\), \(\int^{\infty}[a(t)]^{-1}dt=\infty\), \(f\in C({\mathbb{R}},{\mathbb{R}})\), \(f(x)/x\geq\gamma>0\) for all \(x\neq0\). Necessary conditions for nonoscillation of solutions of (1) are given. Some oscillation criteria for this equation are obtained.
scientific article; zbMATH DE number 1067200
scientific article