A priori estimates for non-coercive Dirichlet problems with subquadratic gradient terms

We deal with some quasilinear elliptic problems posed in a bounded smooth convex domain Omega subset of RN( N >= 3), namely [GRAPHICS] . where the data satisfy [GRAPHICS] . We provide sufficient conditions on f, mu(allowing mu to vanish on partial derivative Omega) that yield the sharp estimate.lambda broken vertical bar broken vertical bar mu broken vertical bar broken vertical bar L-infinity (Omega) <= Cfor any bounded solution uwith..(0,.1), which is the non-coercive regime. The estimate leads to remarkable consequences such as a multiplicity result and a precise asymptotic behavior of the bounded but blowing upsolutions as lambda -> 0(+). (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).