Small solutions of operator equations

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

Chapter 5 in Approximate Solution of Operator Equations, 1972, pp 322-463 from Springer

Abstract: 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 20.1 $$f(\lambda ,x) = 0.$$ Assuming that 20.2 $$f({\lambda _0},{x_0}) = 0,$$ 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 (search for similar items in EconPapers)
Date: 1972
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DOI: 10.1007/978-94-010-2715-1_5

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