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- Title
Necessary and sufficient conditions for oscillation of nonlinear first-order forced differential equations with several delays of neutral type.
- Authors
Pinelas, Sandra; Santra, Shyam S.
- Abstract
In this work, necessary and sufficient conditions are obtained such that every solution of nonlinear neutral first-order differential equations with several delays of the form (x (t) + r (t) x (t - τ) ) ′ + ∑ i = 1 m ϕ i (t) H (x (t - σ i)) = f (t) \bigl{(}x(t)+r(t)x(t-\tau)\bigr{)}^{\prime}+\sum_{i=1}^{m}\phi_{i}(t)H\bigl{(}% x(t-\sigma_{i})\bigr{)}=f(t) is oscillatory or tends to zero as t → ∞. {t\rightarrow\infty.} This problem is considered in various ranges of the neutral coefficient r. Finally, some illustrating examples are presented to show that feasibility and effectiveness of main results.
- Subjects
FUNCTIONAL differential equations; NONLINEAR oscillations; DELAY differential equations; DIFFERENTIAL equations
- Publication
Analysis (0174-4747), 2019, Vol 39, Issue 3, p97
- ISSN
0174-4747
- Publication type
Article
- DOI
10.1515/anly-2018-0010