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 differential equations with mixed nonlinearities. (English) Zbl 1171.34338
The authors study the oscillatory behavior of delay differential equations with mixed nonlinearities $$\multline (r(t)|u'(t)|^{\alpha-1}u'(t))' + q_0(t)|u[\tau_0(t)]|^{\alpha-1}u[\tau_0(t)] + q_1(t)|u[\tau_1(t)]|^{\beta-1}u[\tau_1(t)]\\ + q_2(t)|u[\tau_2(t)]|^{\gamma-1}u[\tau_2(t)]=0,\endmultline$$ where $\gamma>\alpha>\beta>0$. Obtained criteria generalize earlier ones.

34K11Oscillation theory of functional-differential equations
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
Full Text: DOI
[1] Agarwal, R. P.; Shieh, S. L.; Yeh, C. C.: Oscillation criteria for second-order retarded differential equations, Math. comput. Model. 26, 1-11 (1997) · Zbl 0902.34061 · doi:10.1016/S0895-7177(97)00141-6
[2] Chern, J. L.; Lian, W. Ch.; Yeh, C. C.: Oscillation criteria for second order half-linear differential equations with functional arguments, Publ. math. Debrecen 48, 209-216 (1996) · Zbl 1274.34193
[3] Džurina, J.; Stavroulakis, I. P.: Oscillation criteria for second-order delay differential equations, Appl. math. Comput. 140, 445-453 (2003) · Zbl 1043.34071 · doi:10.1016/S0096-3003(02)00243-6
[4] Elbert, Á.: A half-linear second order differential equation, Colloquia math. Soc. 30, 153-180 (1979) · Zbl 0511.34006
[5] Á. Elbert, Oscillation and nonoscillation theorems for some nonlinear ordinary differential equations, in: Ordinary and Partial Differential Equations, Lecture Notes in Mathematics, vol. 964, 1982, pp. 187 -- 212. · Zbl 0528.34034
[6] Hardy, G. H.; Littlewood, J. E.; Polya, G.: Inequalities, (1952) · Zbl 0047.05302
[7] Kusano, T.; Naito, Y.: Oscillation and nonoscillation criteria for second order quasilinear differential equations, Acta math. Hungar. 76, 81-99 (1997) · Zbl 0906.34024 · doi:10.1007/BF02907054
[8] Kusano, T.; Naito, Y.; Ogata, A.: Strong oscillation and nonoscillation of quasilinear differential equations of second order, Diff. eqs. Dyn. syst. 2, 1-10 (1994) · Zbl 0869.34031
[9] Kusano, T.; Yoshida, N.: Nonoscillation theorems for a class of quasilinear differential equations of second order, J. math. Anal. appl. 189, 115-127 (1995) · Zbl 0823.34039 · doi:10.1006/jmaa.1995.1007
[10] Mirzov, D. D.: On some analogs of Sturm’s and Kneser’s theorems for nonlinear systems, J. math. Anal. appl. 53, 418-425 (1976) · Zbl 0327.34027 · doi:10.1016/0022-247X(76)90120-7
[11] Mirzov, D. D.: On the oscillation of solutions of a system of differential equations, Math. zametki 23, 401-404 (1978) · Zbl 0423.34047
[12] Sun, Y. G.; Meng, F. W.: Note on the paper of džurina and stavroulakis, Appl. math. Comput. 174, 1634-1641 (2006) · Zbl 1096.34048 · doi:10.1016/j.amc.2005.07.008