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)
Positive solutions for nonlinear eigenvalue problems. (English) Zbl 0876.34023

The authors are concerned with determining values of λ (eigenvalues), for which there exist positive solutions of the boundary value problem

(1 λ )u '' +λa(t)f(u)=0,0<t<1,(2)u(0)=u(1)=0,

where f:[0,)[0,) is continuous; a:[0,1][0,) is continuous and does not vanish identically on any subinterval, and

f 0 =lim x0 (f(x)/x),f =lim x (f(x)/x)

exist. To research the problem (1 λ ), (2) the Krasnosel’skij methods of solutions of nonlinear operator equations in a space with a cone are applicable.


MSC:
34B15Nonlinear boundary value problems for ODE
34B27Green functions
34B24Sturm-Liouville theory
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators