TY - JOUR
T1 - Semicycles and correlated asymptotics of oscillatory solutions to second-order delay differential equations
AU - Braverman, Elena
AU - Domoshnitsky, Alexander
AU - Stavroulakis, John Ioannis
N1 - Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2024/3/15
Y1 - 2024/3/15
N2 - We obtain several new comparison results on the distance between zeros and local extrema of solutions for the second order delay differential equation x″(t)+p(t)x(t−τ(t))=0,t≥swhere τ:R→[0,+∞), p:R→R are Lebesgue measurable and uniformly essentially bounded, including the case of a sign-changing coefficient. We are thus able to calculate upper bounds on the semicycle length, which guarantee that an oscillatory solution is bounded or even tends to zero. Using the estimates of the distance between zeros and extrema, we investigate the classification of solutions in the case p(t)≤0,t∈R.
AB - We obtain several new comparison results on the distance between zeros and local extrema of solutions for the second order delay differential equation x″(t)+p(t)x(t−τ(t))=0,t≥swhere τ:R→[0,+∞), p:R→R are Lebesgue measurable and uniformly essentially bounded, including the case of a sign-changing coefficient. We are thus able to calculate upper bounds on the semicycle length, which guarantee that an oscillatory solution is bounded or even tends to zero. Using the estimates of the distance between zeros and extrema, we investigate the classification of solutions in the case p(t)≤0,t∈R.
KW - Comparison theorems
KW - Delay
KW - Oscillation
KW - Second-order delay equations
KW - Semicycle
UR - http://www.scopus.com/inward/record.url?scp=85174591262&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2023.127875
DO - 10.1016/j.jmaa.2023.127875
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AN - SCOPUS:85174591262
SN - 0022-247X
VL - 531
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 127875
ER -