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Keywords:
half-linear differential equation; oscillatory solutions
half-linear differential equation; oscillatory solutions
Summary:
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 $.
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