Dynamical systems method (DSM) for nonlinear equations in Banach spaces
| dc.creator | Ramm, A. G. | |
| dc.date | 2004-10-21 | |
| dc.date.accessioned | 2026-07-07T05:13:36Z | |
| dc.date.available | 2026-07-07T05:13:36Z | |
| dc.description | Let $F:X\to X$ be a $C^2_\loc$ map in a Banach space $X$, and $A$ be its Frèchet derivative at the element $w:=w_\ve$, which solves the problem $(\ast) \dotw=-A^{-1}_\ve(F(w)+\ve w)$, $w(0)=w_0$, where $A_\ve:=A+\ve I$. Assume that $\|A^{-1}_\ve\|\leq c \ve^{-k}$, $0<k\leq 1$, $0<\ve>\ve_0$. Then $(\ast)$ has a unique global solution, $w(t)$, there exists $w(\infty)$, and $(\ast\ast) F(w(\infty))+\ve w(\infty)=0$. Thus the DSM (Dynamical Systems Method) is justified for equation $(\ast\ast)$. The limit of $w_\ve$ as $\ve\to 0$ is studied. | |
| dc.identifier | https://arxiv.org/abs/math/0410479 | |
| dc.identifier | http://arxiv.org/abs/math/0410479 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72966 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47J05, 47J06, 47J25 | |
| dc.title | Dynamical systems method (DSM) for nonlinear equations in Banach spaces | |
| dc.type | text |