Second-Order Differential Equation with Multiple Delays: Oscillation Theorems and Applications

Abstract EN

Differential equations of second order appear in physical applications such as fluid dynamics, electromagnetism, acoustic vibrations, and quantum mechanics.

In this paper, necessary and sufficient conditions are established of the solutions to second-order half-linear delay differential equations of the form ςyu′ya′+∑j=1mpjyucjϑjy=0 for y≥y0, under the assumption ∫∞ςη−1/adη=∞.

We consider two cases when acj, where a and cj are the quotient of two positive odd integers.

Two examples are given to show effectiveness and applicability of the result.