A DSM proof of surjectivity of monotone nonlinear mappings
arXiv:0804.33913 citationsh-index: 15
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Simplifies a known proof in monotone operator theory for mathematicians.
The authors prove surjectivity of twice Frechet differentiable monotone operators under coercivity conditions using the Dynamical Systems Method, providing a simpler proof of a known result.
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.