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)
Existence result of second-order differential equations with integral boundary conditions at resonance. (English) Zbl 1180.34016

The paper concerns the boundary value problem

x '' (t)=f(t,x(t),x ' (t)),0<t<1,
x ' (0)= 0 1 h(t)x ' (t)dt,x ' (1)= 0 1 g(t)x ' (t)dt·

It is assumed that the functions h and g are continuous and nonnegative and such that the conditions 0 1 h(t)dt=1 and 0 1 g(t)dt=1 hold. The linear operator L, Lx:=x '' , defined on the subspace of functions that belong to the Sobolev space W 2,1 (0,1) and satisfy the boundary conditions is a Fredholm operator with index zero when the functions h and g satisfy a condition formulated in the preliminary part of the paper. Moreover, its kernel is two-dimensional.

Next, a fixed point theorem due to J. Mawhin [Topological degree methods in nonlinear boundary value problems. Regional Conference Series in Mathematics. No. 40. R.I.: The American Mathematical Society (1979; Zbl 0414.34025)] is recalled. The existence of at least one solution of the boundary value problem is proved when certain conditions are satisfied. They are formulated in the main result which proof is based on Mawhin’s fixed point theorem. An example is presented.

MSC:
34B10Nonlocal and multipoint boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations