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)
Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem. (English) Zbl 1032.34040

The author provides new existence results for the periodic boundary value problem

x '' =f(t,x),x(0)=x(T),x ' (0)=x ' (T),(1)

where f is a Carathéodory function. The proofs are based on the Krasnoselskii fixed-point theorem for completely continuous operators in a Banach space that exhibits a cone compression and expansion, and on the sign behaviour of Green’s function of the linearized equation.

The main results are contained in two theorems which give conditions guaranteeing the existence of a positive solution to (1). Modified assertions for negative solutions are shown.

As applications of these general results, the author obtains new existence results for equations with jumping nonlinearities and for equations with a repulsive or attractive singularity in the origin. Weak singularities are considered here, too.

34C25Periodic solutions of ODE
34B16Singular nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE