Second-Order Differential Equation: Oscillation Theorems and Applications

Abstract EN

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 ac, 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.