Uniqueness results for pseudomonotone problems with p > 2

Juan Casado-Díaz (1) , François Murat (2) , Alessio Porretta (3)

1 EDAN US - Departamento de Ecuaciones Diferenciales y Analisis Numerico
2 LJLL - Laboratoire Jacques-Louis Lions
3 DIPMAT - Dipartimento di Matematica [Roma II]

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 satisfies 0 < α ≤ b(x,s) ≤ β < +∞. We show 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. In 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.
This paper has been published in C. R. Acad. Sci. Paris, Série I, 344, (2007), pp. 487-492.

Domaines: Equations aux dérivées partielles [math.AP]

Juan Casado-Díaz, François Murat, Alessio Porretta. Uniqueness results for pseudomonotone problems with p > 2. C.R. Acad. Sci. Paris série I, 2005. ⟨hal-00139812⟩