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Our purpose is to analyze a first order nonlinear differential equation with advanced arguments. Then, some sufficient conditions for the oscillatory solutions of this equation are presented. Our results essentially improve two conditions in the paper “Oscillation tests for nonlinear differential equations with several nonmonotone advanced arguments” by N. Kilıç, Ö. Öcalan and U. M. Özkan. Also we give an example to illustrate our results.

Oscillation criteria based on a new weighted function for linear matrix Hamiltonian systems.

Guo, Yingxin, Wang, Junchang (2011)

Discrete Dynamics in Nature and Society

Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations.

Akin-Bohner, Elvan, Bohner, Martin, Saker, Samir H. (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Oscillation criteria for a class of nonlinear differential equations of third order

N. Parhi, P. Das (1992)

Annales Polonici Mathematici

Oscillation criteria are obtained for nonlinear homogeneous third order differential equations of the form $y^{'''} + q (t) y^{'} + p (t) y^{α} = 0$ and y”’ + q(t)y’ + p(t)f(y) = 0, where p and q are real-valued continuous functions on [a,∞), f is a real-valued continuous function on (-∞, ∞) and α > 0 is a quotient of odd integers. Sign restrictions are imposed on p(t) and q(t). These results generalize some of the results obtained earlier in this direction.

Oscillation criteria for a class of second-order nonlinear differential equations with damping term.

Ouyang, Zigen, Zhong, Jichao, Zou, Shuliang (2009)

Abstract and Applied Analysis

Oscillation criteria for certain nonlinear fourth order equations.

Taylor, W.E.jun. (1983)

International Journal of Mathematics and Mathematical Sciences

Oscillation criteria for differential equation $y^{(4)} + P (t) y^{''} + R (t) y^{'} + Q (t) y = 0$

Ján Regenda (1984)

Mathematica Slovaca

Oscillation criteria for forced neutral differential equations

Said R. Grace, Bikkar S. Lalli (1994)

Czechoslovak Mathematical Journal

Oscillation criteria for forced nonlinear elliptic equations of arbitrary order

Peter Švaňa (1988)

Časopis pro pěstování matematiky

Oscillation criteria for fourth order half-linear differential equations

Jaroslav Jaroš, Kusano Takaŝi, Tomoyuki Tanigawa (2020)

Archivum Mathematicum

Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form $(| y^{''} |^{α} sgn y^{''})^{''} + q (t) {| y |}^{α} sgn y = 0, t \geq a > 0, A$ where $α > 0$ is a constant and $q (t)$ is positive continuous function on $[a, \infty)$ , are given in terms of an increasing continuously differentiable function $ω (t)$ from $[a, \infty)$ to $(0, \infty)$ which satisfies $\int_{a}^{\infty} 1 / (t ω (t)) d t < \infty$ .

Oscillation criteria for fourth-order linear differential equations

Ján Regenda (1979)

Mathematica Slovaca

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