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@article{1678221,
author = {Hasil, Petr and Veselý, Michal},
article_location = {San Diego},
article_number = {1},
doi = {http://dx.doi.org/10.1016/j.jmaa.2020.124585},
keywords = {Linear differential equations; Oscillation theory; Non-oscillation; Oscillation tests; Slowly varying functions; Periodic coefficients},
language = {eng},
issn = {0022-247X},
journal = {Journal of Mathematical Analysis and Applications},
title = {New conditionally oscillatory class of equations with coefficients containing slowly varying and periodic functions},
url = {https://doi.org/10.1016/j.jmaa.2020.124585},
volume = {494},
year = {2021}
}
TY - JOUR
ID - 1678221
AU - Hasil, Petr - Veselý, Michal
PY - 2021
TI - New conditionally oscillatory class of equations with coefficients containing slowly varying and periodic functions
JF - Journal of Mathematical Analysis and Applications
VL - 494
IS - 1
SP - 1-22
EP - 1-22
PB - ACADEMIC PRESS INC ELSEVIER SCIENCE
SN - 0022247X
KW - Linear differential equations
KW - Oscillation theory
KW - Non-oscillation
KW - Oscillation tests
KW - Slowly varying functions
KW - Periodic coefficients
UR - https://doi.org/10.1016/j.jmaa.2020.124585
L2 - https://doi.org/10.1016/j.jmaa.2020.124585
N2 - The main result of this paper is a straightforward oscillation test for linear differential equations whose coefficients consist of products of periodic and slowly varying continuous functions. The attention is paid to the case when the slowly varying parts of the coefficients are unbounded. In particular, using the presented oscillation test, we identify a very general type of conditionally oscillatory equations together with the threshold value of the coefficients (the critical setting on the border of oscillation and non-oscillation). Hence, our results supply a class of linear equations with solved oscillation behaviour which can be used as testing equations and as a starting point to the oscillation theory of the corresponding half-linear and more general non-linear and partial differential equations with unbounded coefficients.
ER -
HASIL, Petr a Michal VESELÝ. New conditionally oscillatory class of equations with coefficients containing slowly varying and periodic functions. \textit{Journal of Mathematical Analysis and Applications}. San Diego: ACADEMIC PRESS INC ELSEVIER SCIENCE, roč.~494, č.~1, s.~1-22. ISSN~0022-247X. doi:10.1016/j.jmaa.2020.124585. 2021.
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