Oscillation and nonoscillation of two terms linear and half-linear equations of higher order

R. Oinarov, L. N. Gumilev Eurasian National University, Kazakhstan
S. Y. Rakhimova, L. N. Gumilev Eurasian National University, Kazakhstan

E. J. Qualitative Theory of Diff. Equ., No. 49. (2010), pp. 1-15.

Abstract: In this paper we investigate the properties of nonoscillation for the equation $$(-1)^{n}(\rho(t)|y^{(n)}|^{p-2}y^{(n)})^{(n)}-v(t)|y|^{p-2}y=0,$$ where $1<p<\infty$ and ${v}$ is a non-negative continuous function and ${\rho}$ is a positive $n$-times continuously differentiable function on the half-line $[0,\infty)$. When the principle of reciprocity is used for the linear equation ($p=2$) we suppose that the functions ${v}$ and ${\rho}$ are positive and $n$-times continuously differentiable on the half-line $[0,\infty)$.

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