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Zbl 1056.39016
Atici, F.Merdivenci; Cabada, A.; Otero-Espinar, V.
Criteria for existence and nonexistence of positive solutions to a discrete periodic boundary value problem.
(English)
[J] J. Difference Equ. Appl. 9, No. 9, 765-775 (2003). ISSN 1023-6198

The paper deals with a discrete nonlinear equation $$-\Delta[p(n-1)\Delta u(n-1)] + q(n)u(n) = \lambda f(n,u(n)).$$ The existence of positive solutions of a periodic boundary value problem $$u(0)=u(N), \quad p(0)\Delta u(0) = p(N)\Delta u(N),$$ where $\{u(n)\}_{n=0}^{N+1}$ is a desired solution, for the system is proved. Moreover, conditions for the nonexistence of positive solutions are defined.
[Marat Akhmet (Ankara)]
MSC 2000:
*39A12 Discrete version of topics in analysis
39A10 Difference equations
39A11 Stability of difference equations

Keywords: positive solutions; discrete periodic boundary value conditions; index theory; lower and upper solutions

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