Oscillation and non-oscillation of some neutral differential equations of odd order (Q1196606)

The authors consider neutral differential equations of the form \((x(t)- cx(t-\tau))'-p(t)x(g(t))=0\), \((x(t)+cx(t-\tau))'-p(t)x(g(t))=p(t)\), \((x(t)-h(t)f_ 1(x(\tau(t))))^{(n)}+p(t)f_ 2(x(g(t))=0\); they give some conditions which assure that the previous equations have oscillatory and nonoscillatory solutions. In the proof they use fixed point theorems which combine both the Banach contraction mapping principle and the Schauder fixed point theorem.