Oscillation criteria for fourth order half-linear differential equations

Jaroš, Jaroslav ; Takaŝi, Kusano ; Tanigawa, Tomoyuki

Archivum mathematicum, Tome 56 (2020) no. 2, pp. 115-125.

Résumé

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 $.

Détail

DOI : 10.5817/AM2020-2-115

Classification : 34C10
Keywords: half-linear differential equation; oscillatory solutions