Nonlinear elliptic anisotropic problem involving non-local boundary conditions with variable exponent and graph data

Abstract

We study a nonlinear elliptic anisotropic problem involving non-local conditions. We also consider variable exponent and general maximal monotone graph datum at the boundary. We prove the existence and uniqueness of weak solution to the problem.

Anisotropic problem with non-local boundary conditions and measure data

“…where the right-hand side f ∈ L ∞ (Ω) and ρ a maximal monotone graph on R such that D(ρ) = Im(ρ) = R and 0 ∈ ρ(0), d ∈ R, by using the technique of monotone operators in Banach spaces (see [21]) and approximation methods. There are two difficulties associated with the study of problem P (ρ, µ, d).…”