Existence of nonoscillatory solutions for \(n\)th order nonlinear neutral functional differential equations (Q1378731)

The authors consider high-order nonlinear neutral functional differential equations \[ \Biggl[y(t)- \sum^l_{i= 1}A_i(t)y(t- \gamma_i)\Biggr]^{(n)}+ (-1)^{n+ 1}f(t,y(g_1(t)),\dots, y(g_m(t)))= 0\tag{1} \] and \[ \Biggl[y(t)- \sum^l_{i= 1}B_i(t,y(t- \sigma_i(t)))\Biggr]^{(n)}+ (-1)^{n+ 1}f(t,y(g_1(t)),\dots, y(g_m(t)))= 0,\tag{2} \] where \(\gamma_i\) is a constant, \(A_i\), \(B_i\), \(\sigma_i\), \(g_j\), and \(f\) are continuous mappings for \(i= 1,2,\dots,l\); \(j= 1,2,\dots,m\), and give some new sufficient criterions of existence of nonoscillatory solutions for the equations (1) and (2). These results are a meaningful extension for the corresponding problems of neutral equations.