Electron. J. Diff. Eqns., Vol. 2005(2005), No. 09, pp. 1-16.

Nonlinear Neumann problems on bounded Lipschitz domains

Abdelmajid Siai

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.

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Abdelmajid Siai
Institut Préparatoire aux Études d'Ingénieurs de Nabeul
8050 Nabeul, Tunisie
email: abdelmejid.s@gnet.tn

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