Existence of a nonoscillatory solution to a second-order linear neutral delay equation
The following neutral functional-differential equation is considered \[ {d^2\over dt^2}(x(t)+px(t-\tau)) +Q_1(t)x(t-\sigma_1) -Q_2(t)x(t-\sigma_2)=0, \] with \(p\in \mathbb{R}\), \(\tau\in(0,\infty)\), \(\sigma_1,\sigma_2\in[0,\infty)\) and \(Q_1, Q_2\in C([t_0,\infty), \mathbb{R}^+)\). Sufficient conditions for the existence of a nonoscillatory solution are obtained. They are expressed in terms of the integrals \(\int^\infty sQ_i(s) ds<\infty\), \(i=1,2\).
neutral functional-differential equation
scientific article; zbMATH DE number 1246328
scientific article