Geodesic
Oscillation criteria for fourth order half-linear differential equations
Archivum mathematicum, Tome 56 (2020) no. 2, pp. 115-125 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form \begin{equation*} \big (|y^{\prime \prime }|^\alpha {\rm sgn\ } y^{\prime \prime }\big )^{\prime \prime } + q(t)|y|^\alpha {\rm sgn}\ y = 0, \quad t \ge a > 0, A \end{equation*} where $\alpha > 0$ is a constant and $q(t)$ is positive continuous function on $[a,\infty )$, are given in terms of an increasing continuously differentiable function $\omega (t)$ from $[a,\infty )$ to $(0,\infty )$ which satisfies $\int _a^\infty 1/(t\omega (t))\,dt \infty $.
Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form \begin{equation*} \big (|y^{\prime \prime }|^\alpha {\rm sgn\ } y^{\prime \prime }\big )^{\prime \prime } + q(t)|y|^\alpha {\rm sgn}\ y = 0, \quad t \ge a > 0, A \end{equation*} where $\alpha > 0$ is a constant and $q(t)$ is positive continuous function on $[a,\infty )$, are given in terms of an increasing continuously differentiable function $\omega (t)$ from $[a,\infty )$ to $(0,\infty )$ which satisfies $\int _a^\infty 1/(t\omega (t))\,dt \infty $.
DOI : 10.5817/AM2020-2-115
Classification : 34C10
Keywords: half-linear differential equation; oscillatory solutions 
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Jaroš, Jaroslav; Takaŝi, Kusano; Tanigawa, Tomoyuki. Oscillation criteria for fourth order half-linear differential equations. Archivum mathematicum, Tome 56 (2020) no. 2, pp. 115-125. doi: 10.5817/AM2020-2-115

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