Abstract
The article considers the invertibility of nonlinear operators which map a metric space or a weak metric space into a Banach space. It is shown that a nonlinear operator close to the invertible nonlinear operator is invertible. The analogous result for an operator distant from invertible operator is proved by parameter continuation method. Some properties of resolvent set in nonlinear case are established. A new approach to resolvent set and spectrum of nonlinear operators is offered.
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Trenogin, V.A. (1998). Invertibility of Nonlinear Operators and Parameter Continuation Method. In: Ramm, A.G. (eds) Spectral and Scattering Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1552-8_12
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DOI: https://doi.org/10.1007/978-1-4899-1552-8_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1554-2
Online ISBN: 978-1-4899-1552-8
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