Solvability of discrete Dirichlet problem via lower and upper functions method

Abstract

We use the lower and upper functions method to prove the existence of a solution of the Dirichlet problem

where , , is positive and is continuous. Provided f fulfils certain sign conditions we get the solvability of the problem for each .

Keywords:

• Dirichlet discrete BVP
• Lower and upper functions
• Brouwer fixed point theorem
• Existence

Keywords:

• 39A12
• 39A10
• 39A70

Acknowledgements

Supported by the Council of Czech Government MSM 6198959214.