New product-type oscillation criteria for first-order linear differential equations with several nonmonotone arguments

Autor: Emad R. Attia, Hassan A. El-Morshedy
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Boundary Value Problems, Vol 2023, Iss 1, Pp 1-19 (2023)
Druh dokumentu: article
ISSN: 1687-2770
DOI: 10.1186/s13661-023-01743-0
Popis: Abstract We use an improved technique to establish new sufficient criteria of product type for the oscillation of the delay differential equation x ′ ( t ) + ∑ l = 1 m b l ( t ) x ( σ l ( t ) ) = 0 , t ≥ t 0 , $$\begin{aligned} x'(t)+\sum_{l=1}^{m} b_{l}(t)x\bigl(\sigma _{l}(t)\bigr)= 0,\quad t\geq t_{0}, \end{aligned}$$ with b l , σ l ∈ C ( [ t 0 , ∞ ) , [ 0 , ∞ ) ) $b_{l},\sigma _{l}\in C([t_{0},\infty ),[0,\infty ))$ such that σ l ( t ) ≤ t $\sigma _{l}(t)\leq t$ and lim t → ∞ σ l ( t ) = ∞ $\lim_{t \rightarrow \infty} \sigma _{l}(t)=\infty $ , l = 1 , 2 , … , m $l=1,2,\ldots,m$ . The obtained results are applicable for the nonmonotone delay case. Their strength is supported by a detailed practical example.
Databáze: Directory of Open Access Journals
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