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@article{1542756, author = {Hasil, Petr and Veselý, Michal}, article_location = {New York}, article_number = {NOV 15 2019}, 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}, language = {eng}, issn = {0096-3003}, journal = {Applied Mathematics and Computation}, title = {Modified Prüfer angle and conditional oscillation of perturbed linear and half-linear differential equations}, url = {https://www.sciencedirect.com/science/article/pii/S0096300319304928}, volume = {361}, year = {2019} }
TY - JOUR ID - 1542756 AU - Hasil, Petr - Veselý, Michal PY - 2019 TI - Modified Prüfer angle and conditional oscillation of perturbed linear and half-linear differential equations JF - Applied Mathematics and Computation VL - 361 IS - NOV 15 2019 SP - 788-809 EP - 788-809 PB - ELSEVIER SCIENCE INC SN - 00963003 KW - Half-linear equations KW - Conditional oscillation KW - Oscillation constant KW - Riccati equation KW - p-Laplacian KW - Prüfer angle UR - https://www.sciencedirect.com/science/article/pii/S0096300319304928 L2 - https://www.sciencedirect.com/science/article/pii/S0096300319304928 N2 - 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. ER -
HASIL, Petr a Michal VESELÝ. Modified Prüfer angle and conditional oscillation of perturbed linear and half-linear differential equations. \textit{Applied Mathematics and Computation}. New York: ELSEVIER SCIENCE INC, 2019, roč.~361, NOV 15 2019, s.~788-809. ISSN~0096-3003. Dostupné z: https://dx.doi.org/10.1016/j.amc.2019.06.027.
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