## Positive solutions for second-order nonlinear discrete periodic boundary value problems.(English)Zbl 1240.39016

Summary: A kind of discrete periodic boundary value problems with parameter $$\lambda$$ is studied. Under different combinations of sublinearity and superlinearity of nonlinear term $$f$$, this paper discusses how the number of positive solutions varies while $$\lambda$$ varies, as well as the uniqueness of solutions and the dependence of solutions on the parameter $$\lambda$$.

### MSC:

 39A12 Discrete version of topics in analysis 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 39A22 Growth, boundedness, comparison of solutions to difference equations 39A10 Additive difference equations