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Positive solutions for a class of singular discrete Dirichlet problems with a parameter. (English) Zbl 1448.39019

Summary: By applying variational arguments and the lower and upper solution method, we obtain several criteria for the existence of positive solutions to a class of singular discrete Dirichlet problems with a parameter. Our results cover the cases when the nonlinear function in the equation is superlinear, asymptotically linear, and sublinear. We provide several examples to illustrate our results.

MSC:

39A27 Boundary value problems for difference equations
39A12 Discrete version of topics in analysis
35B09 Positive solutions to PDEs
35A15 Variational methods applied to PDEs
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References:

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