Oscillation and non-oscillation results for solutions of perturbed half-linear equations
| Authors | |
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| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Mathematical Methods in the Applied Sciences |
| MU Faculty or unit | |
| Citation | HASIL, Petr and Michal VESELÝ. Oscillation and non-oscillation results for solutions of perturbed half-linear equations. Mathematical Methods in the Applied Sciences. 111 RIVER ST, HOBOKEN 07030-5774: Wiley, 2018, vol. 41, No 9, p. 3246-3269. ISSN 0170-4214. Available from: https://dx.doi.org/10.1002/mma.4813. |
| web | http://dx.doi.org/10.1002/mma.4813 |
| Doi | http://dx.doi.org/10.1002/mma.4813 |
| Keywords | conditional oscillation; half-linear equations; oscillation constant; oscillation theory; Prüfer angle; Riccati equation |
| Description | The purpose of this paper is to describe the oscillatory properties of second-order Euler-type half-linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non-oscillation of the considered equations, including the so-called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations. |
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