Necessary and sufficient conditions for oscillation of the solutions of even order differential equations

Cheng Jin-Fa; Chu Yu-Ming

doi:10.33993/jnaat411-965

Authors

Cheng Jin-Fa Xiamen University, China
Chu Yu-Ming Huzhou Teachers College, China

DOI:

https://doi.org/10.33993/jnaat411-965

Keywords:

oscillation, nonoscillatory solution, even order differential equation

Abstract views: 217

Abstract

In this paper, we establish several necessary and sufficient conditions for oscillation of the solutions of the following even order differential equation\[x^{(n)}(t) + q(t)x^\gamma (t) = 0, \quad \mbox{$n$ is even},\]where $ q(t) \in C([t_0 ,\infty ),{\mathbb R}^ + )$ and $\gamma$ is the quotient of odd positive integers.

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