On the existence of bilateral solutions to an anisotropic nonlinear coupled elliptic system
Journal of Nonlinear and Variational Analysis · 2025
The existence of a bilateral solution at a given height to the strongly nonlinear and degenerate problem A(u) = ρ(u)|∇ϕ| 2 , div(ρ(u)∇ϕ) = 0 in Ω, u = 0 and ϕ = ϕ 0 on ∂ Ω, where A is a Leray-Lions operator, is proved in the framework of anisotropic Sobolev space.The bilateral solution is obtained through a double approximation process, with the first one being a penalization technique.