Multiple Ordered Solutions for a Class of Problems Involving the 1-Laplacian Operator - Santos, Gelson dos; Figueiredo, Giovany M.; Pimenta, Marcos T. O. [UNESP] (Springer Nature, 2022)
In this paper, we use minimax methods, comparison arguments, and an approximation result to show the existence and multiplicity of solutions for the following class of problems: {-Δ1v=λf(v)inΩ,v≥0inΩ,v=0on∂Ω,where Ω is a bounded smooth domain of RN, N≥ 1 , λ> 0 is a parameter and the non-linearity f: R→ R is a continuous function that can change sign and satisfies an area condition.
Keywords: 1-Laplacian operator; Quasilinear elliptic operator