×

zbMATH — the first resource for mathematics

Existence of multiple positive solutions for a nonlocal boundary value problem. (English) Zbl 1071.34023
Summary: Sufficient conditions are given for the existence of multiple positive solutions of a boundary value problem of the form \(x''(t)+ q(t)f(x(t))= 0\), \(t\in[0,1]\), \(x(0)= 0\) and \(x(1)=\int^\beta_\alpha x(s)dg(s)\), with \(0<\alpha< \beta< 1\). A weaker boundary value problem is used to get information on the corresponding integral operator. Then, the results follow by applying the Krasnoselskij fixed-point theorem on a suitable cone.

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI