Oscillation of solutions to odd-order nonlinear neutral functional differential equations

Abstract

In this note, we establish some new comparison theorems and Philos-type criteria for oscillation of solutions to the odd-order nonlinear neutral functional differential equation $$ [x(t)+p(t)x(au(t))]^{(n)}+q(t)x^alpha(sigma(t))=0, $$ where $0leq p(t)leq p_0<infty$ and $alphageq1$.

Keywords

• Odd-order
• neutral differential equation
• oscillation
• asymptotic behavior