Asymptotic behavior of the solutions of a third-order nonlinear differential equation. (English. Ukrainian original) Zbl 1390.34086
J. Math. Sci., New York 229, No. 4, 412-424 (2018); translation from Neliniĭni Kolyvannya 20, No. 1, 74-84 (2017).
Consider the scalar differential equation
\[
(x''+ p(t) x)'+ p(t) x'+ q(t)\,f(x)= 0,\tag{\(*\)}
\]
where \(p\), \(q\), \(f\) are continuous, \(q(t)>0\) and \(xf(x)>0\) for \(x\neq 0\).
The authors study solutions of \((*)\) that are continuable and nontrivial. They derive conditions under which these solutions are oscillatory or nonoscillatory. Some necessary and sufficient relationships between the square integrability of the first and the second derivatives are also presented.
The authors study solutions of \((*)\) that are continuable and nontrivial. They derive conditions under which these solutions are oscillatory or nonoscillatory. Some necessary and sufficient relationships between the square integrability of the first and the second derivatives are also presented.
Reviewer: Klaus R. Schneider (Berlin)
MSC:
| 34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
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