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Positive solutions of discrete \((n,p)\) boundary value problems. (English) Zbl 0893.39001
Consider the boundary value problem \[ \Delta^ny +\lambda F(k,y, \Delta y, \dots, \Delta^{n-2} y)= \lambda G(k,y,\Delta y, \dots, \Delta^{n-1}y), \quad k=n-1, \dots, N,\tag{1} \] \[ \Delta^i y(0)=0, \quad 0\leq i\leq n-2, \quad \Delta^p y(N+n-p) =0, \tag{2} \] where \(n\geq 2\), \(\lambda >0\) and \(p\) is a fixed integer \((0\leq p\leq n-1)\). The author obtains conditions on \(\lambda\) for which the problem (1), (2) has a positive solution, i.e. she determines the set of eigenvalues.

MSC:
39A10 Additive difference equations
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