Abstract
We generalize a recent global implicit function theorem from [8] to the case of a mapping acting between Banach spaces. Considerations related to duality mapping and to certain auxiliary functional are used in the proof together with the local implicit function theorem and mountain pass geometry. An application to integro-differential systems is given.
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Galewski, M., Koniorczyk, M. On a global implicit function theorem and some applications to integro-differential initial value problems. Acta Math. Hungar. 148, 257–278 (2016). https://doi.org/10.1007/s10474-016-0589-y
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DOI: https://doi.org/10.1007/s10474-016-0589-y
Key words and phrases
- local implicit function theorem
- global implicit function theorem
- duality mapping
- mountain pass geometry
- integro-differential equation