# 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 of some nonlocal boundary value problems. (English) Zbl 1072.34014

For two 4-point BVP

${u}^{\text{'}\text{'}}\left(t\right)+g\left(t\right)f\left(u\left(t\right)\right)=0\phantom{\rule{1.em}{0ex}}\text{a.e.}\phantom{\rule{4.pt}{0ex}}\text{on}\phantom{\rule{4.pt}{0ex}}\left[0,1\right],$
${u}^{\text{'}}\left(0\right)=0,\phantom{\rule{1.em}{0ex}}u\left(1\right)={\alpha }_{1}u\left({\eta }_{1}\right)+{\alpha }_{2}u\left({\eta }_{2}\right),$

or

$u\left(0\right)=0,\phantom{\rule{1.em}{0ex}}u\left(1\right)={\alpha }_{1}u\left({\eta }_{1}\right)+{\alpha }_{2}u\left({\eta }_{2}\right),$

the authors determine a region in the $\left({\alpha }_{1},\phantom{\rule{0.166667em}{0ex}}{\alpha }_{2}\right)$-plane which ensures the existence of positive solutions. Further, they conclude that one can obtain the existence of positive solutions for an $m$-point boundary value problem under the weaker assumption that all parameters occurring in the boundary conditions are not required to be positive. Hence, their results allow more general behavior on $f$ than being either sub- or superlinear.

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ODE 34B18 Positive solutions of nonlinear boundary value problems for ODE 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 34B15 Nonlinear boundary value problems for ODE