Criteria for existence and nonexistence of positive solutions to a discrete periodic boundary value problem. (English) Zbl 1056.39016

Atici, F. Merdivenci; Cabada, A.; Otero-Espinar, V.

J. Difference Equ. Appl. 9, No. 9, 765-775 (2003).

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.

Reviewer: Marat Akhmet (Ankara)

MSC:

39A12	Discrete version of topics in analysis
39A10	Additive difference equations
39A11	Stability of difference equations (MSC2000)

Keywords:

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

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