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Positive solutions for second-order three-point eigenvalue problems. (English) Zbl 1204.34029

Summary: By means of the fixed point index theorem in cones, we get an existence theorem concerning the existence of a positive solution for the second-order three-point eigenvalue problem
\[ x''(t)+\lambda f(t,x(t))=0,\quad 0\leq t\leq 1,\;x(0)=0,\;x(1)=x(\eta), \]
where \(\lambda\) is a parameter. An illustrative example is given to demonstrate the effectiveness of the obtained result.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B09 Boundary eigenvalue problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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References:

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