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Nonlinear eigenvalue problems for BVPs of second-order difference equations. (English) Zbl 1120.39012

Using the Krasnoselskii fix point theorem, the authors give sufficient conditions for the existence of at least one positive solution of the boundary value problem \(x(0) = x(T+2)= 0\) for the second-order difference equation \[ \Delta^2 x(t-1) + \lambda f(t,x(t)) = 0, \;t \in \{1,2,...,T+1\}, \] where \(\Delta x(t) = x(t+1) - x(t),\) \(T \geq 2\) is a given integer.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
34L30 Nonlinear ordinary differential operators
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