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)
A note on Nasr’s and Wong’s papers. (English) Zbl 1042.34096
Summary: In the case of oscillatory potentials, we give sufficient conditions for the oscillation of a forced nonlinear second-order differential equations with delayed argument of the form $$x^{\prime\prime}(t)+ q(t)\vert x(\tau(t)) \vert^\gamma \operatorname{sgn} x(\tau(t))= f(t)$$ in the linear ($\gamma$=1) and the superlinear ($\gamma>1$) case. See, {\it A. H. Nasr} [Proc. Am. Math. Soc. 126, 123--125 (1998; Zbl 0891.34038)] and {J. S. W. Wong} [J. Math. Anal. Appl. 231, 235--240 (1999; Zbl 0922.34029)].

34K11Oscillation theory of functional-differential equations
Full Text: DOI
[1] Kartsatos, A. G.: On the maintenance of oscillation of n-th order equations under the effect of a small forcing term. J. differential equations 10, 355-363 (1971) · Zbl 0216.11504
[2] Kartsatos, A. G.: Maintenance of oscillations under the effect of a periodic forcing term. Proc. amer. Math. soc. 33, 377-382 (1972) · Zbl 0234.34040
[3] El-Sayed, M. A.: An oscillation criterion for a forced second order linear differential equation. Proc. amer. Math. soc. 118, 813-817 (1993) · Zbl 0777.34023
[4] Nasr, A. H.: Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential. Proc. amer. Math. soc. 126, 123-125 (1998) · Zbl 0891.34038
[5] Wong, J. S. W.: Oscillation criteria for a forced second-order linear differential equation. J. math. Anal. appl. 231, 235-240 (1999) · Zbl 0922.34029
[6] Keener, M. S.: Solutions of a certain linear nonhomogeneous second order differential equations. Appl. anal. 1, 57-63 (1971) · Zbl 0215.43802
[7] Teufel, H.: Forced second order nonlinear oscillations. J. math. Anal. appl. 40, 148-152 (1972) · Zbl 0211.12001
[8] Skidmore, A.; Leighton, W.: On the differential equation y”+$p(x)y=f(x)$. J. math. Anal. appl. 43, 46-55 (1973) · Zbl 0287.34031
[9] Skidmore, A.; Bowers, J. J.: Oscillatory behavior of solutions of y”+$p(x)y=f(x)$. J. math. Anal. appl. 49, 317-323 (1975) · Zbl 0312.34025
[10] Rainikin, S. M.: Oscillation theorems for second order nonhomogeneous linear differential equations. J. math. Anal. appl. 53, 550-553 (1976) · Zbl 0328.34033
[11] Wong, J. S. W.: Second order nonlinear forced oscillations. SIAM J. Math. anal. 19, 667-675 (1988) · Zbl 0655.34023
[12] Nasr, A. H.: Necessary and sufficient conditions for the oscillation of forced nonlinear second order differential equations with delayed argument. J. math. Anal. appl. 212, 51-59 (1997) · Zbl 0884.34075