Some new oscillation criteria of third-order half-linear neutral difference equations

T. Gopal; G. Ayyappan; R. Arul

doi:10.26637/MJM0803/0100

Abstract

In this article, we introduce the oscillation of all solutions of third-order half-linear neutral difference equation(OSTOHLDE)
$$
\Delta\left(g(n)(\Delta(h(n) \Delta z(n)))^\alpha\right)+f(n) y^\alpha(n+1)=0,
$$
where $z(n)=y(n)+e(n) y(n-k)$ and $\alpha$ is a ratio of odd positive integers(PI). Our results are new and complement to the existing ones.

Keywords:

Third-order, half-linear difference equation(DE), neutral, oscillation

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

T. Gopal Department of Mathematics, Periyar University, Salem-636011, Tamil Nadu, India.
G. Ayyappan Department of Mathematics, Periyar University College of Arts and Science, Pappireddipatti -636905, Tamil Nadu, India.
R. Arul Department of Mathematics, Kandaswami Kandar’s College, Velur-638182, Tamil Nadu, India.

Pages: 1301-1305
Date Published: 01-07-2020
Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

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