HASIL, Petr and Michal VESELÝ. Oscillation and non-oscillation criteria for linear and half-linear difference equations. Journal of Mathematical Analysis and Applications. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017, vol. 452, No 1, p. 401-428. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2017.03.012. |
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@article{1375985, author = {Hasil, Petr and Veselý, Michal}, article_location = {SAN DIEGO}, article_number = {1}, doi = {http://dx.doi.org/10.1016/j.jmaa.2017.03.012}, keywords = {half-linear difference equations; oscillation theory; conditional oscillation; oscillation constant; Riccati technique; adapted Riccati equation}, language = {eng}, issn = {0022-247X}, journal = {Journal of Mathematical Analysis and Applications}, title = {Oscillation and non-oscillation criteria for linear and half-linear difference equations}, volume = {452}, year = {2017} }
TY - JOUR ID - 1375985 AU - Hasil, Petr - Veselý, Michal PY - 2017 TI - Oscillation and non-oscillation criteria for linear and half-linear difference equations JF - Journal of Mathematical Analysis and Applications VL - 452 IS - 1 SP - 401-428 EP - 401-428 PB - ACADEMIC PRESS INC ELSEVIER SCIENCE SN - 0022247X KW - half-linear difference equations KW - oscillation theory KW - conditional oscillation KW - oscillation constant KW - Riccati technique KW - adapted Riccati equation N2 - We find very general classes of linear and half-linear difference equations which are conditionally oscillatory. We identify the critical oscillation constant whose value implies the oscillation or non-oscillation of studied equations. Our results are divided into oscillatory and non-oscillatory theorems which determine the critical oscillation constant for coefficients given by sequences having mean values. In addition, our approach enables to analyse also the oscillatory properties of equations whose coefficients are not given by sequences with mean values. We point out that the obtained results are new even for linear equations with periodic coefficients. Such consequences are formulated at the end of this paper. ER -
HASIL, Petr and Michal VESELÝ. Oscillation and non-oscillation criteria for linear and half-linear difference equations. \textit{Journal of Mathematical Analysis and Applications}. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017, vol.~452, No~1, p.~401-428. ISSN~0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2017.03.012.
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