English

A DSM proof of surjectivity of monotone nonlinear mappings

Numerical Analysis 2008-04-23 v1

Abstract

We prove that if FF is twice Frechet differentiable and coercivity conditions hold, then FF is surjective, i.e., the equation F(u)=hF(u)=h is solvable for every hHh\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.

Keywords

Cite

@article{arxiv.0804.3391,
  title  = {A DSM proof of surjectivity of monotone nonlinear mappings},
  author = {A. G. Ramm},
  journal= {arXiv preprint arXiv:0804.3391},
  year   = {2008}
}