A DSM proof of surjectivity of monotone nonlinear mappings

Details A DSM proof of surjectivity of monotone nonlinear mappings A DSM proof of surjectivity of monotone nonlinear mappings

2008-04-21

arxiv.org/abs/0804.3391v1

Mathematics

Numerical Analysis

Scientific paper

We prove that if $F$ is twice Frechet differentiable and coercivity conditions hold, then $F$ is surjective, i.e., the equation $F(u)=h$ is solvable for every $h\in H$. This is a basic result in the theory of monotone operators. Our aim is to give a simple and short proof of this result based on the Dynamical Systems Method (DSM), developed in the monograph A.G. Ramm, Dynamical systems method, Elsevier, Amsterdam, 2007.

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