The asymptotic behavior of the solutions of the Cauchy problem generated by φ-accretive operators

The purpose of this paper is to study the asymptotic behavior of the solutions of certain type of differential inclusions posed in Banach spaces. In particular, we obtain the abstract result on the asymptotic behavior of the solution of the boundary value problem (Graphics) where Omega is a bounded open domain in R-n with smooth boundary partial derivative Omega, f (t, x) is a given L-1 -function on]0, infinity[ x Omega, gamma >= 1 and 1 <= p < infinity. Delta(p) represents the p-Laplacian operator, partial derivative/partial derivative eta is the associated Neumann boundary operator and beta a maximal monotone graph in R x R with 0 is an element of beta(0). (c) 2005 Elsevier Inc. All rights reserved.