Oscillatory Properties of Solutions of Generalized Emden–Fowler Equations

Abstract

This work deals with the study of oscillatory properties of solutions of the equation

$$\displaystyle{{u}^{(n)}(t) + p(t)\,\big\vert u(\sigma (t)){\big\vert }^{\mu (t)}\mathrm{sign}u(\sigma (t)) = 0,}$$

where $p \in L_{\mathrm{loc}}(R_{+};R_{-})$, $\mu \in C(R_{+};(0,+\infty ))$, $\sigma \in C(R_{+};R_{+})$, and σ(t) ≥ t for t ∈ R ₊. In this chapter, new sufficient (necessary and sufficient) conditions for essentially nonlinear functional differential equations to have Property B are established.