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)
Nonlocal conjugate type boundary value problems of higher order. (English) Zbl 1181.34025

In this interesting paper, the author studies the nonlocal boundary value problem

u (n) (t)+g(t)f(t,u(t))=0,t(0,1),u (k) (0)=0,0kn-2,u(1)=α[u],

where α[·] is a linear functional on C[0,1] given by a Riemann-Stieltjes integral, namely

α[u]= 0 1 u(s)dA(s),

with dA a signed measure. This formulation is quite general and covers classical m-point boundary conditions and integral conditions as special cases. The author proves, under suitable growth conditions on the nonlinearity f, existence of multiple positive solutions.

Interesting features of this paper are that the theory is illustrated with explicit examples, including a 4-point problem with coefficients with both signs, and that all the constants that appear in the theoretical results are explicitly determined.

The methodology involves classical fixed point index theory and makes extensive use of the results in J. R. L. Webb and G. Infante [NoDEA, Nonlinear Differ. Equ. Appl. 15, No. 1–2, 45–67 (2008; Zbl 1148.34021)], J. R. L. Webb and K. Q. Lan [Topol. Methods Nonlinear Anal. 27, 91–115 (2006; Zbl 1146.34020)], J. R. L. Webb and G. Infante [J. Lond. Math. Soc., II. Ser. 74, No. 3, 673–693 (2006; Zbl 1115.34028)].

MSC:
34B10Nonlocal and multipoint boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
34B27Green functions
47N20Applications of operator theory to differential and integral equations