Strong comparison principle and multiplicity results for Finsler p-Laplace equations - Das, Monti; Tiwari, Sweta (Topological Methods in Nonlinear Analysis, 2026)
In this paper, we consider the family of problems equation* cases - Δ_H, p u = f_λ(x, u) & in Ω, u > 0 & in Ω, u = 0 & on Ω, cases equation* where Ω is a smooth bounded domain in R ^N, N2 , λ is a real parameter and the anisotropic Finsler p-Laplacian operator Δ_H, p with 1< p< N, is defined as Δ_H, p u: = div(H( abla u)^p-1 abla_η H( abla u)). The non-linear term f_λ Ω × R → R is the sum of a sublinear and a superlinear term. We establish the strong comparison principle and extend the well-known Brezis-Nirenberg result concerning local minimization in C_0^1 and W_0^1,p to the framework of the Finsler p-Laplace operator. Under various growth assumptions on the non-linear term f_λ (x, s) and the real parameter λ, we establish the existence, non-existence and multiplicity of solutions.