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Zbl 0937.39001
Agarwal, Ravi P.; O'Regan, Donal
Nonpositone discrete boundary value problems. (English)
[J] Nonlinear Anal., Theory Methods Appl. 39, No.2, A, 207-215 (2000). ISSN 0362-546X

The boundary value problem $$\Delta^2 y(i-1)+\mu f\bigl(i,y(i) \bigr)=0,$$ $i=1,2, \dots,T$, $y(0)= y(T+1)=0$, is investigated under certain conditions, in particular $f(i,0)\le 0$, also for $i=0$ and $i=T+1$. For sufficiently small positive $\mu$ the existence of a positive solution is proved by means of the conical shell fixed point theorem.
[Lothar Berg (Rostock)]

MSC 2000:: *39A10 Difference equations

Keywords: discrete boundary value problems; nonpositive solutions; nonnegative solutions; conical shell fixed point theorem; positive solution

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