Existence and comparison results for difference \(\phi\)-Laplacian boundary value problems with lower and upper solutions in reverse order
For a strictly increasing \(\varphi:\mathbb{R} \to\mathbb{R}\) with Lipschitzian \(\varphi^{-1}\) and a negative parameter \(M\) with small \(|M |\) the difference equation \(-\Delta [\varphi(\Delta u(k))]+ Mu(k+1)= \sigma (k)\) is studied under various boundary conditions. In particular existence, uniqueness and comparison results are derived. Generalizations to a difference equation with a second nonlinearity are pointed out.
scientific article; zbMATH DE number 1749667