Opuscula Math. 35, no. 4 (), 485-497
http://dx.doi.org/10.7494/OpMath.2015.35.4.485
Opuscula Mathematica

# Oscillation criteria for third order nonlinear delay differential equations with damping

Abstract. This note is concerned with the oscillation of third order nonlinear delay differential equations of the form $\left( r_{2}(t)\left( r_{1}(t)y^{\prime}(t)\right)^{\prime}\right)^{\prime}+p(t)y^{\prime}(t)+q(t)f(y(g(t)))=0.\tag{$$\ast$$}$ In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007), 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010), 756-762], the authors established some sufficient conditions which insure that any solution of equation $$(\ast)$$ oscillates or converges to zero, provided that the second order equation $\left( r_{2}(t)z^{\prime }(t)\right)^{\prime}+\left(p(t)/r_{1}(t)\right) z(t)=0\tag{$$\ast\ast$$}$ is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation $$(\ast)$$ oscillates if equation $$(\ast\ast)$$ is nonoscillatory. We also establish results for the oscillation of equation $$(\ast)$$ when equation $$(\ast\ast)$$ is oscillatory.
Keywords: oscillation, third order, delay differential equation.
Mathematics Subject Classification: 34C10, 39A10.
Cite this article as:
Said R. Grace, Oscillation criteria for third order nonlinear delay differential equations with damping, Opuscula Math. 35, no. 4 (2015), 485-497, http://dx.doi.org/10.7494/OpMath.2015.35.4.485

Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.