zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Oscillation of second-order delay dynamic equations on time scales. (English) Zbl 1180.34069

Summary: By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations

p (t) x Δ (t) γ Δ +q(t)fx τ ( t )=0

on a time scale 𝕋, here γ1 is a quotient of odd positive integers with p and q real-valued positive rd-continuous functions defined on 𝕋. Our results improve and extend some results established by S. H. Saker [J. Comput. Appl. Math. 177, No. 2, 375–387 (2005; Zbl 1082.34032)] but also unify the oscillation of the second order nonlinear delay differential equation and the second order nonlinear delay difference equation.

34K11Oscillation theory of functional-differential equations
34N05Dynamic equations on time scales or measure chains
39A10Additive difference equations
[1]Hilger, S.: Analysis on measure chains–a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)
[2]Agarwal, R.P., Bohner, M., O’Regan, D., Peterson, A.: Dynamic equations on time scales: a survey. J. Comput. Appl. Math. 141, 1–26 (2002) · Zbl 1020.39008 · doi:10.1016/S0377-0427(01)00432-0
[3]Bohner, M., Peterson, A.: Dynamic Equations on Time Scales, an Introduction with Applications. Birkhauser, Boston (2001)
[4]Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhauser, Boston (2003)
[5]Bohner, M., Saker, S.H.: Oscillation of second order nonlinear dynamic equations on time scales. Rocky Mt. J. Math. 34, 1239–1254 (2004) · Zbl 1075.34028 · doi:10.1216/rmjm/1181069797
[6]Erbe, L.H.: Oscillation results for second order linear equations on a time scale. J. Differ. Equ. Appl. 8, 1061–1071 (2002) · Zbl 1021.34012 · doi:10.1080/10236190290015317
[7]Saker, S.H.: Oscillation criteria of second-order half-linear dynamic equations on time scales. J. Comput. Appl. Math. 177, 375–387 (2005) · Zbl 1082.34032 · doi:10.1016/j.cam.2004.09.028
[8]Agarwal, R.P., Bohner, M., Saker, S.H.: Oscillation of second order delay dynamic equations. Can. Appl. Math. Q. 13, 1–18 (2005)
[9]Erbe, L., Peterson, A., Saker, S.H.: Oscillation criteria for second-order nonlinear delay dynamic equations. J. Math. Anal. Appl. 333, 505–522 (2007) · Zbl 1125.34046 · doi:10.1016/j.jmaa.2006.10.055
[10]Han, Z., Sun, S., Shi, B.: Oscillation criteria for a class of second order Emden-Fowler delay dynamic equations on time scales. J. Math. Anal. Appl. 334, 847–858 (2007) · Zbl 1125.34047 · doi:10.1016/j.jmaa.2007.01.004
[11]Sahiner, Y.: Oscillation of second-order delay differential equations on time scales. Nonlinear Anal. TMA 63, 1073–1080 (2005) · Zbl 1224.34294 · doi:10.1016/j.na.2005.01.062
[12]Zhang, B.G., Shanliang, Z.: Oscillation of second order nonlinear delay dynamic equations on time scales. Comput. Math. Appl. 49, 599–609 (2005) · Zbl 1075.34061 · doi:10.1016/j.camwa.2004.04.038