zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential. (English) Zbl 1030.34034

Summary: New oscillation criteria established for the forced second-order nonlinear equation with oscillatory potential

p (t) y ' (t) ' +q(t)fy ( t )=g(t)

are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of [t 0 ,), rather than on the whole half-line. Our results are of a high degree of generality and sharper than some previous results and handle the cases which are not covered by known results. Moreover, these results can also be applied to the extreme such as t 0 q(s)ds=-.


MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory