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Positive solutions to an \(n\)th order right focal boundary value problem. (English) Zbl 1115.34027

Summary: The existence of a positive solution is obtained for the \(n^{th}\) order right focal boundary value problem \[ y^{(n)}=f(x,y), \quad 0 < x \leq 1. \]
\[ y^{(i)}(0)=y^{(n-2)}(p)=y^{(n-1)}(1)=0,\quad i=0,\dots, n-3, \] where \(\frac{1} {2}<p<1\) is fixed and where \(f(x,y)\) is singular at \(x=0, y=0\), and possibly at \(y=\infty\). The method applies a fixed-point theorem for mappings that are decreasing with respect to a cone.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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