Structural stability for nonlinear Neumann boundary p(u)-Laplacian problem

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Résumé

This paper is devoted to the study of nonlinear homogeneous Neumann boundary p(u)-Laplacian problem of the form
{b(u)−diva(x,u,∇u)=fa(x,u,∇u).η=0in Ωon ∂Ω,
where Ω is a smooth bounded open domain in ℝN, N≥3 and η the outer unit normal vector on ∂Ω. The existence and uniqueness results of weak solution and the structural stability result are obtained by approximation method and convergent sequences in terms of Young measure

Mots-clés

variable exponent p(u)-Laplacian; Young measure; homogeneous Neumann boundary condition; continuous dependence; weak solution