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Small solutions of operator equations

  • M. A. Krasnosel’skii
  • G. M. Vainikko
  • P. P. Zabreiko
  • Ya. B. Rutitskii
  • V. Ya. Stetsenko
Chapter
  • 196 Downloads

Abstract

Let E, F and Λ be Banach spaces, f(λ, x) an operator defined for \({\left\| {\lambda - {\lambda _0}} \right\|_\Lambda } \le a{\left\| {x - {x_0}} \right\|_E} \le b\) with values in F. Consider the equation
$$f(\lambda ,x) = 0.$$
(20.1)
Assuming that
$$f({\lambda _0},{x_0}) = 0,$$
(20.2)
we wish to find a solution x*(λ) of equation (20.1) which is close to x0 when λ is close to λ0.

Keywords

Bifurcation Point Operator Equation Simple Solution Asymptotic Approximation Formal Power Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Wolters-Noordhoff Publishing, Groningen 1972

Authors and Affiliations

  • M. A. Krasnosel’skii
  • G. M. Vainikko
  • P. P. Zabreiko
  • Ya. B. Rutitskii
  • V. Ya. Stetsenko

There are no affiliations available

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