J. Nonl. Evol. Equ. Appl. 2017 (2), pp. 13-25, published on June 13, 2017:

Uniqueness result of entropy solution to nonlinear Neumann problems with variable exponent and L¹-data

Département de Mathématiques, Centre Régional des Métiers de l’Education et de Formation, El Jadida, Maroc

Département de Mathématiques, Faculté des Sciences, Université Mohammed V, Agdal, Rabat, Maroc

Received on December 20, 2015; final version on May 25, 2016
Accepted on May 22, 2016 (with modifications), final version on June 17, 2016

Communicated by Alexander Pankov

Abstract. Our aim in this paper is to study the uniqueness question of the nonlinear Neumann problems with variable exponent\|u\|^p(x)−2u − div [ \|∇u − Θ(u)\|^p(x)−2 (∇u − Θ(u)) ] + α(u) = f in Ω, where Ω is a connected open bounded set in R^N, p(.) is a continuous function defined on $\bar Ω$ with p(.) ∈ L^∞(Ω) and p(x) > 1 for all x ∈ $\bar Ω$. We will have in mind especially the case when initial data are in L¹.
Keywords:	Nonlinear elliptic problem, Neumann-type boundary, entropy solution, variable exponent, uniqueness.
2010 Mathematics Subject Classification: 35J60, 35J65, 35J92.