Oscillatory criteria via linearization of half-linear second order delay differential equations

Abstract

In the paper, we study oscillation of the half-linear second order delay differential equations of the form \[\left(r(t)(y'(t))^{\alpha}\right)'+p(t)y^{\alpha}(\tau(t))=0.\] We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered equation which leads to new oscillatory criteria. The presented results essentially improve existing ones.

Keywords

• second order differential equations
• delay
• monotonic properties
• linearization
• oscillation