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

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.


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