Existence results for the 1-Laplacian problem with a critical concave–convex nonlinearity - Pimenta, Marcos T. O. [UNESP]; Carranza, Yino B. C. [UNESP]; Figueiredo, Giovany M. (Springer Nature, 2024)
In this paper, we study a critical concave–convex type problem involving the 1-Laplacian operator in a general Lipschitz-continuous domain. We show an existence result using an approximation method, in which the solution is obtained as limit of solutions to p-Laplacian type problems. To overcome the lack of compactness, a version of the well-known Concentration Compactness Principle of Lions is used.
Keywords: 1-Laplacian operator; critical growth; singular nonlinearity