On Oscillation and Asymptotic Behaviour of Solutions of Forced First Order Neutral Differential Equations

Proceedings Mathematical Sciences

N Parhi¹  R N Rath² 

[1] Department of Mathematics, Berhampur University, Berhampur 0 00, India$$;Department of Mathematics, Govt. Science College, Chatrapur 00, India$$

关键词: Oscillation;    nonoscillation;    neutral equations;    asymptotic behaviour.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, sufficient conditions have been obtained under which every solution of$[y(t)± y(t-𝜏)]'±mathcal{Q}(t)G(y(t-𝜎)) = f(t),quad t≥ 0$,oscillates or tends to zero or to ± ∞ as 𝑡 → ∞. Usually these conditions are stronger thanegin{equation*}intlimits_0^∞mathcal{Q}(t)dt=∞.ag{*}end{equation*}An example is given to show that the condition $(*)$ is not enough to arrive at the above conclusion. Existence of a positive (or negative) solution of$[y(t)-y(t-𝜏)]'+mathcal{Q}(t)G(y(t-𝜎))=f(t)$is considered.

【 授权许可】

Unknown