Second-Order Differential Equation: Oscillation Theorems and Applications

Abstract

Differential equations of second order appear in a wide variety of applications in physics, mathematics, and engineering. In this paper, necessary and sufficient conditions are established for oscillations of solutions to second-order half-linear delay differential equations of the form ςyu′ya′+pyucϑy=0, for y≥y0, under the assumption ∫∞ςη-1/a=∞. Two cases are considered for a c, where a and c are the quotients of two positive odd integers. Two examples are given to show the effectiveness and applicability of the result.