Positive solutions to an Nth order right focal boundary value problem

M. Maroun, University of Louisiana at Monroe, Monroe, LA, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 4. (2007), pp. 1-17.

Abstract: The existence of a positive solution is obtained for the $n^{th}$ order right focal boundary value problem $y^{(n)}=f(x,y)$, $0 < x \leq 1$, $y^{(i)}(0)=y^{(n-2)}(p)=y^{(n-1)}(1)=0, i=0,\cdots, n-3$, 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.

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