Dynamical systems method and a homeomorphism theorem
| dc.creator | Ramm, A. G. | |
| dc.date | 2004-08-14 | |
| dc.date.accessioned | 2026-07-07T05:11:17Z | |
| dc.date.available | 2026-07-07T05:11:17Z | |
| dc.description | Let $F$ be a nonlinear map in a real Hilbert space $H$. Suppose that $\sup_{u\in B(u_0,R)}$ $\|[F'(u)]^{-1}\|\leq m(R)$, where $B(u_0,R)=\{u:\|u-u_0\|\leq R\}$, $R>0$ is arbitrary, $u_0\in H$ is an element. If $\sup_{R>0}\frac{R}{m(R)}=\infty$, then $F$ is surjective. If $\|[F'(u)]^{-1}\|\leq a\|u\|+b$, $a\geq 0$ and $b>0$ are constants independent of $u$, then $F$ is a homeomorphism of $H$ onto $H$. The last result is known as an Hadamard-type theorem, but we give a new simple proof of it based on the DSM (dynamical systems method). | |
| dc.identifier | https://arxiv.org/abs/math/0408192 | |
| dc.identifier | http://arxiv.org/abs/math/0408192 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72188 | |
| dc.subject | Functional Analysis | |
| dc.subject | 6J15, 47H17, 58C15 | |
| dc.title | Dynamical systems method and a homeomorphism theorem | |
| dc.type | text |