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Existence of positive solutions for boundary value problems of second-order functional difference equations. (English) Zbl 1066.39015

The author studies the existence of positive solutions for the following boundary value problem (BVP) formulated for a second order difference equation \[ -\Delta^2y(n-1) = f(n,y(w(n)))\;,\;n\in [a,b] \]
\[ \alpha y(n-1) - \beta\Delta y(n-1) = \zeta(n)\;,\;n\in [\tau_1,a] \]
\[ \gamma y(n) + \delta\Delta y(n) = \eta(n)\;,\;n\in [b,\tau_2] \] with \(a\), \(b\) (\(b>a+1\)) integers and \(\Delta\) the forward difference operator, a discrete analogue of a similar BVP for a second-order functional differential equation. Two existence theorems are proved and relations to previous results are established.

MSC:

39A12 Discrete version of topics in analysis
39A11 Stability of difference equations (MSC2000)
34K10 Boundary value problems for functional-differential equations
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References:

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