Nonlinear Neumann problems on bounded Lipschitz domains
Abdelmajid Siai · DOAJ (DOAJ: Directory of Open Access Journals) · 2005
We prove existence and uniqueness, up to a constant, of an entropy solution to the nonlinear and non homogeneous Neumann problem $$displaylines{ -mathop{ m div}[ mathbf{a}(., abla u)] +eta (u)=f quadhbox{ in } Omega cr frac{partial u}{partial u _{mathbf{a}}}+gamma (au u)=g quad hbox{on } partial Omega,. }$$ Our approach is based essentially on the theory of m-accretive operators in Banach spaces, and in order preserving properties.