Modified Prüfer angle and conditional oscillation of perturbed linear and half-linear differential equations
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Applied Mathematics and Computation |
| MU Faculty or unit | |
| Citation | |
| Web | Full Text |
| Doi | http://dx.doi.org/10.1016/j.amc.2019.06.027 |
| Keywords | Half-linear equations; Conditional oscillation; Oscillation constant; Riccati equation; p-Laplacian; Prüfer angle |
| Description | The research and results described in this paper belong to the qualitative theory of differential equations (more precisely, the partial differential equations with the one-dimensional p-Laplacian). Using a method whose core is formed by the Prüfer technique, we identify a borderline case between oscillatory and non-oscillatory equations. Moreover, we are able to decide whether the studied equations are oscillatory or not even in the so-called critical (i.e., the borderline) case. The advantage of our approach is the fact that we obtain new and strong results for linear and half-linear equations (i.e., the equations with the one-dimensional p-Laplacian) at the same time. In addition, we are able to work with equations whose coefficients are non-constant and non-periodic. The novelty of our results is documented by examples and corollaries. |
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