Dynamical systems method and surjectivity of nonlinear maps (Q1776778)

In continuation of his earlier work on the dynamical systems method [J. Phys. A, Math. Gen. 36, No. 16, L249--L254 (2003; Zbl 1048.65056); Commun. Nonlinear Sci. Numer. Simul. 9, No. 4, 383--402 (2004; Zbl 1073.47056)], the author applies the method for proving the surjectivity of a \(C^2_{\text{loc}}\)-map \(F : H \rightarrow H\) on a real Hilbert space \(H\) under the conditions \(\sup_{u \in B(u_0,R)} \| F'(u)^{-1} \| \leq m(R)\) and \({\limsup}_{R > 0} {{R} \over {m(R)}} = \infty\).