Nonlinear multivalued homogeneous Robin boundary p(u)-laplacian problem

Stanislas Ouaro; Noufou Sawadogo

doi:10.56947/amcs.v24.308

Authors

Stanislas Ouaro Laboratoire de Mathematiques et d'Informatique (LA.M.I), UFR Sciences Exactes et Appliquees, Universite Joseph KI ZERBO, Burkina Faso
Noufou Sawadogo Universite de Ouahigouya, UFR. Sciences et Technologie, Departement de Mathématiques et informatique, Burkina Faso

DOI:

https://doi.org/10.56947/amcs.v24.308

Keywords:

Variable exponent p(u)-laplacian, Robin boundary condition, bounded Radon diffuse measure, maximal monotone graph, renormalized solution

Abstract

We study the following nonlinear multivalued Robin boundary p(u)− laplacian problem β(u) − diva(x, u, ∇u) ∋ f in Ω, a(x, u, ∇u).η = −|u|r(x,u)−2u on ∂Ω. The existence and uniqueness of solutions for L1-data f are established.