Dynamical systems method (DSM) for nonlinear equations in Banach spaces

Details Dynamical systems method (DSM) for nonlinear equations in Banach spaces Dynamical systems method (DSM) for nonlinear equations in Banach spaces

2004-10-21

arxiv.org/abs/math/0410479v1

Mathematics

Functional Analysis

Scientific paper

Let $F:X\to X$ be a $C^2_\loc$ map in a Banach space $X$, and $A$ be its Fr\`echet 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 $\|A^{-1}_\ve\|\leq c \ve^{-k}$, $0\ve_0$. 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.

Affiliated with

Also associated with

No associations

Rating

Dynamical systems method (DSM) for nonlinear equations in Banach spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamical systems method (DSM) for nonlinear equations in Banach spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical systems method (DSM) for nonlinear equations in Banach spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-425131