Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 09, pp. 1-16.

Title: Nonlinear Neumann problems on bounded Lipschitz domains

Author: Abdelmajid Siai (Institut Prep. aux Etudes d'Ingenieurs, Tunisie)

Abstract: 
 We prove existence and uniqueness, up to a constant, of an entropy solution
 to the nonlinear and non homogeneous Neumann problem
 $$\displaylines{
  -\mathop{\rm div}[ \mathbf{a}(.,\nabla u)] +\beta (u)=f 
  \quad\hbox{ in } \Omega \cr
  \frac{\partial u}{\partial \nu _{\mathbf{a}}}+\gamma (\tau u)=g \quad
  \hbox{on } \partial \Omega\,.
 }$$
 Our approach is based essentially on the theory of m-accretive operators in
 Banach spaces, and in order preserving properties.

Submitted December 29, 2004. Published January 12, 2005.
Math Subject Classifications: 35J60, 35J70, 47J05.
Key Words: Nonlinear Neumann problem; m-completely accretive operator.