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Positive solutions for third-order three-point nonhomogeneous boundary value problems. (English) Zbl 1163.34313
Summary: In this work, by employing the Guo-Krasnosel’skii fixed point theorem and Schauder’s fixed point theorem, we study the existence and nonexistence of positive solutions to the third-order three-point nonhomogeneous boundary value problem
\begin{aligned} u^{\prime\prime\prime} (t)+ a & (t)f(u(t))=0, \quad 0<t<1 \\ u(0)=u^{\prime} & (0)=0, \qquad u^{\prime}(1) - \alpha u^{\prime}(\eta) = \lambda \end{aligned}
where $$\eta \in (0,1), \alpha \in [0,1/\eta)$$ are constants and $$\lambda \in (0,\infty)$$ is a parameter.

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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