Implicit function theorem in sectorial quasi-neighborhoods
Article in issue: 15 (115), 2008.
Free access
We consider nonlinear operational equation F(x, λ) = 0 with condition F(0,0) = 0. Operator Fx(0,0) is not continuously inversible. We costruct continuous solutions х(λ) → 0 as λ → 0 in open set S of linear normalized space A. Zero belongs to frontier of set S. Solution existence theorems we have illustrated by examples.
sectorial quasi-neighborhoods
\ banach space
\ nonlinear operator equation
\ linear normalized space
\ two-point boundary problem
\ implicit function theorem
Short address: https://sciup.org/147159036
IDS: 147159036 | UDC: 517.9
