Uniqueness results for pseudomonotone problems with p>2

Abstract

We consider a pseudomonotone operator, the model of which is −div(b(x, u)|∇ u| p−2∇ u) with 1 <p< +∞ and b(x, s) a Lipschitz continuous function in s which hold satisfies 0 < α b(x, s) β < +∞. We show that the comparison principle (and therefore the uniqueness for the Dirichlet problem) in two particular cases, namely the one-dimensional case, and the case where at least one of the right-hand sides does not change sign. To the best of our knowledge these results are new for p > 2. Full detailed proofs are given in the present Note. The results continue to hold when Ω is unbounded