On the qualitative behavior of the solutions to second-order neutral delay differential equations

[摘要] Differential equations of second order appear in numerous applications such as fluid dynamics, electromagnetism, quantum mechanics, neural networks and the field of time symmetric electrodynamics. The aim of this work is to establish necessary and sufficient conditions for the oscillation of the solutions to a second-order neutral differential equation. First, we have taken a single delay and later the results are generalized for multiple delays. Some examples are given and open problems are presented.

[学科分类] 电力

[关键词] Oscillation;Non-oscillation;Delay;Neutral;Lebesgue’s Dominated Convergence theorem;Necessary and sufficient conditions