# 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 and multiplicity of solutions for four-point boundary value problems at resonance. (English) Zbl 1070.34026

Under the assumptions $0<\xi ,\eta <1,0 and $a\xi \left(1-b\right)+\left(1-a\right)\left(1-b\eta \right)=0$, using the coincidence degree theory, the authors establish lower and upper solutions for the following BVP

${x}^{\text{'}\text{'}}\left(t\right)=f\left(t,x\left(t\right)\right),\phantom{\rule{0.277778em}{0ex}}t\in \left(0,1\right),\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}x\left(0\right)=ax\left(\xi \right),\phantom{\rule{0.277778em}{0ex}}x\left(1\right)=bx\left(\eta \right)·$

By this way, they obtain some existence and multiplicity results for this problem. The results in this paper generalize those in [R. Ma, Nonlinear Anal., Theory Methods Appl. 53, 777–789 (2003; Zbl 1037.34011)], but the methods used are different from those in above mentioned paper.

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ODE