Address:
Corresponding author: Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, Bratislava, 842 48, Slovakia
Department of Mathematics, Faculty of Science, Hiroshima University, Higashi Hiroshima, 739-8526, Japan
Department of Mathematical Sciences, Osaka Prefecture University, Osaka 599-8531, Japan
E-mail:
jaros@fmph.uniba.sk
kusanot@zj8.so-net.ne.jp
ttanigawa@ms.osakafu-u.ac.jp
Abstract: 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 $.
AMSclassification: primary 34C10.
Keywords: half-linear differential equation, oscillatory solutions.
DOI: 10.5817/AM2020-2-115