Asymptotic behaviour of solutions to $n$-order functional differential equations

Abstract

We establish conditions for the linear differential equation $$ y^{(n)}(t)+p(t)y(g(t))=0 $$ to have property A. Explicit sufficient conditions for the oscillation of the the equation is obtained while dealing with the property A of the equations. A comparison theorem is obtained for the oscillation of the equation with the oscillation of a third order ordinary differential equation.

Keywords

• Oscillatory solution
• nonoscillatory solution
• property A.