The asymptotic behavior of a class of φ-harmonic functions in Orlicz–Sobolev spaces

The asymptotic behavior of the sequence {u n } { u n } of solutions for a class of inhomogeneous problems with prescribed Dirichlet data on the boundary is studied in the setting of Orlicz-Sobolev spaces. We prove that u n →u ∞ u n → u ∞ uniformly in Ω as n→∞ n → ∞ , where u ∞ u ∞ is an ∞-harmonic function satisfying the prescribed Dirichlet data on the boundary.