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)
On multi-point boundary value problems for linear ordinary differential equations with singularities. (English) Zbl 1058.34012

The authors investigate the singular linear differential equation

u (n) = i=1 n p i (t)u (i-1) +q(t)(1)

on [a,b], where the functions p i and q can have singularities at t=a,t=b and t=t 0 (a,b). This means that p i and q are not integrable on [a,b]. Equation (1) is studied with the boundary conditions

u (i-1) (t 0 )=0for1in-1, j=1 n-n 1 α 1j u (j-1) (t 1j )+ j=1 n-n 2 α 2j u (j-1) (t 2j )=0,(2)

or

u (i-1) (a)=0for1in-1, j=1 n-n 0 α j u (j-1) (t j )=0,(3)

where t 1j ,t 2j ,t j are certain interior points in (a,b). The authors introduce the Fredholm property for these problems which means that the unique solvability of the corresponding homogeneous problem implies the unique solvability of the nonhomogeneous problem for every q which is weith-integrable on [a,b]. Then, for the solvability of a problem having the Fredholm property, it sufficies to show that the corresponding homogeneous problem has only the trivial solution. In this way, the authors prove main theorems on the existence of a unique solution of (1),(2) and of (1),(3). Examples verifying the optimality of the conditions in various corollaries are shown as well.

MSC:
34B10Nonlocal and multipoint boundary value problems for ODE
34B05Linear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE