Asymptotic behavior up to the second order term of solutions to quasilinear elliptic singular problems. (November 2016) - Giarrusso, Ester; Porru, Giovanni
Abstract: Let Ω ⊂ R N be a bounded smooth domain. We prove the existence of a positive solution to the problem Δ u = − u − γ | ∇ u | q in Ω, u = 0 on ∂ Ω, with γ > 1 and 0 < q < 1 . Furthermore, for γ > 3 and 0 < q ≤ ( γ − 3 ) / ( γ − 2 ) we find asymptotic expansions up to the second order of a solution u in terms of the distance from x to the boundary ∂ Ω .