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)
Bounded perturbations with multiple delays of forced harmonic oscillators at resonance. (English) Zbl 0758.34056
The problem of existence of $2\pi$-periodic solutions for the two delay differential equations $x''(t)+x(t)+h\sb 1(x(t-r))+h\sb 2(x(t-s))=p(t)$ and $x''(t)+x(t)+h(x(t-r))+g(x'(t-s)=p(t)$ is investigated. The results which are proved by using a slight modification of an abstract result due to {\it R. K. Nagle} and {\it Z. Sinkala} [Differential Equations: Stability and Control, Proc. Int. Conf., Colorado Springs/CO (USA) 1989, Lect. Notes Pure Appl. Math. 127, 401-408 (1990; Zbl 0711.34053)] extend some known results obtained for bounded perturbations of forced harmonic oscillators at resonance and for similar problems where the perturbations involve the derivative of the solution.

34K99Functional-differential equations
34C25Periodic solutions of ODE
34D10Stability perturbations of ODE
34K10Boundary value problems for functional-differential equations
34B15Nonlinear boundary value problems for ODE
34C15Nonlinear oscillations, coupled oscillators (ODE)
70K30Nonlinear resonances (general mechanics)