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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
##### Keywords:
Krasnoselskij fixed-point theorem
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