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We consider a Brezis-Nirenberg problem on the hyperbolic space Hn. By using the stereographic projection, the problem becomes a singular problem on the boundary of the open ball B1(0) ⊂ Rn. Thanks to the Hardy inequality, in a version due to Brezis-Marcus, the difficulty involving singularities can be overcame. We use the mountain pass theorem due to Ambrosetti-Rabinowitz and Brezis-Nirenberg arguments to obtain a nontrivial solution. [ABSTRACT FROM AUTHOR]

In this article, we prove the existence of solutions for some discrete nonlinear difference equations subjected to a potential boundary type condition. We use a variational technique that relies on Szulkin's critical point theory, which ensures the existence of solutions by ground state and mountain pass methods. [ABSTRACT FROM AUTHOR]