Abstract
We investigate transformations of the modified Riccati differential equation and the obtained results we apply in the investigation of oscillatory properties of perturbed half‐linear Euler differential equation. A perturbation is also allowed in the differential term.
Highlights
The half-linear Euler differential equation Φx γp tp Φ xΦ x : |x|p−2x, p > 1, 1.1 with the so-called oscillation constant γp : p − 1 /p p−1 plays an important role in the oscillation theory of the half-linear differential equation rtΦxctΦx 0, 1.2 with the continuous functions r, c, and r t > 0
If n 1 in 1.7, that is, this equation reduces to the so-called Riemann-Weber half-linear differential equation, this equation is oscillatory if β1 > μp and nonoscillatory in the opposite case
In this paper we deal with perturbations of the Euler half-liner differential equation in full generality
Summary
Φ x : |x|p−2x, p > 1, 1.1 with the so-called oscillation constant γp : p − 1 /p p−1 plays an important role in the oscillation theory of the half-linear differential equation rtΦxctΦx 0, 1.2 with the continuous functions r, c, and r t > 0. If n 1 in 1.7 , that is, this equation reduces to the so-called Riemann-Weber half-linear differential equation, this equation is oscillatory if β1 > μp and nonoscillatory in the opposite case. This result was partially extended to half-linear equations in 3. In this paper we deal with perturbations of the Euler half-liner differential equation in full generality. We recall some essentials of the half-linear oscillation theory
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