HASIL, Petr and Michal VESELÝ. Oscillation and non-oscillation criterion for Riemann-Weber type half-linear differential equations. Electronic Journal of Qualitative Theory of Differential Equations. Maďarsko: Electronic Journal of Qualitative Theory of Differential Equations, 2016, vol. 2016, No 59, p. "nestrankovano", 22 pp. ISSN 1417-3875. Available from: https://dx.doi.org/10.14232/ejqtde.2016.1.59. |
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@article{1349539, author = {Hasil, Petr and Veselý, Michal}, article_location = {Maďarsko}, article_number = {59}, doi = {http://dx.doi.org/10.14232/ejqtde.2016.1.59}, keywords = {half-linear equations; Prüfer angle; Riccati equation; oscillation theory; conditional oscillation; oscillation constant; oscillation criterion}, language = {eng}, issn = {1417-3875}, journal = {Electronic Journal of Qualitative Theory of Differential Equations}, title = {Oscillation and non-oscillation criterion for Riemann-Weber type half-linear differential equations}, volume = {2016}, year = {2016} }
TY - JOUR ID - 1349539 AU - Hasil, Petr - Veselý, Michal PY - 2016 TI - Oscillation and non-oscillation criterion for Riemann-Weber type half-linear differential equations JF - Electronic Journal of Qualitative Theory of Differential Equations VL - 2016 IS - 59 SP - "nestrankovano" EP - "nestrankovano" PB - Electronic Journal of Qualitative Theory of Differential Equations SN - 14173875 KW - half-linear equations KW - Prüfer angle KW - Riccati equation KW - oscillation theory KW - conditional oscillation KW - oscillation constant KW - oscillation criterion N2 - By the combination of the modified half-linear Prufer method and the Riccati technique, we study oscillatory properties of half-linear differential equations. Taking into account the transformation theory of half-linear equations and using some known results, we show that the analysed equations in the Riemann-Weber form with perturbations in both terms are conditionally oscillatory. Within the process, we identify the critical oscillation values of their coefficients and, consequently, we decide when the considered equations are oscillatory and when they are non-oscillatory. As a direct corollary of our main result, we solve the so-called critical case for a certain type of half-linear non-perturbed equations. ER -
HASIL, Petr and Michal VESELÝ. Oscillation and non-oscillation criterion for Riemann-Weber type half-linear differential equations. \textit{Electronic Journal of Qualitative Theory of Differential Equations}. Maďarsko: Electronic Journal of Qualitative Theory of Differential Equations, 2016, vol.~2016, No~59, p.~''nestrankovano'', 22 pp. ISSN~1417-3875. Available from: https://dx.doi.org/10.14232/ejqtde.2016.1.59.
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