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Oscillation of first order linear differential equations with several non-monotone delays

Oscillation of first order linear differential equations with several non-monotone delays AbstractConsider the first-order linear differential equation with several retarded argumentsx′(t)+∑k=1npk(t)x(τk(t))=0,t≥t0,$$\begin{array}{}\displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0},\end{array} $$where the functions pk, τk ∈ C([t0, ∞), ℝ+), τk(t) < t for t ≥ t0 and limt→∞τk(t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

Oscillation of first order linear differential equations with several non-monotone delays

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Publisher
de Gruyter
Copyright
© 2018 Attia et al., published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0010
Publisher site
See Article on Publisher Site

Abstract

AbstractConsider the first-order linear differential equation with several retarded argumentsx′(t)+∑k=1npk(t)x(τk(t))=0,t≥t0,$$\begin{array}{}\displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0},\end{array} $$where the functions pk, τk ∈ C([t0, ∞), ℝ+), τk(t) < t for t ≥ t0 and limt→∞τk(t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.

Journal

Open Mathematics – de Gruyter

Published: Feb 23, 2018

Keywords: Oscillation; Differential equations; Non-monotone delays; 34K11; 34K06

References

  • Oscillations of differential equations with deviating arguments
  • Specific properties of solutions of first order differential equations with several delay arguments
  • New oscillation criterion for delay differential equations with non-monotone arguments
  • Oscillation Theory for Functional Differential Equations
  • Oscillations caused by several retarded and advanced arguments
  • Oscillation criteria for differential equations with several retarded arguments
  • On the oscillation of solutions of first order differential equations with retarded arguments
  • When all solutions of x(t) = −Σql(t)x(t − Tl(t)) oscillate
  • Oscillations caused by retarded perturbations of first order linear ordinary differential equations
  • An oscillation criterion for delay differential equations with several non-monotone arguments
  • Oscillation theory of first order functional differential equations with deviating arguments
  • Iterative oscillation tests for differential equations with several non-monotone arguments