Extremal solutions of a class of nonlinear integro-differential equations in Banach spaces
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- by Hong-Kun Xu and Juan J. Nieto PDF
- Proc. Amer. Math. Soc. 125 (1997), 2605-2614 Request permission
Abstract:
The monotone iterative technique is applied to a class of nonlinear first order integro-differential equations in Banach spaces. First a linear system with a “small” nonlinear perturbation is solved using Banach’s Contraction Principle and the technique of Green’s function. Then based upon a comparison result, the existence of minimal and maximal solutions is proved.References
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Additional Information
- Hong-Kun Xu
- Affiliation: Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa
- Email: hkxu@pixie.udw.ac.za
- Juan J. Nieto
- Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain
- Email: amnieto@usc.es
- Received by editor(s): March 13, 1996
- Additional Notes: Part of the paper was announced by the first author at the International Symposium on Methods and Applications of Analysis, City University of Hong Kong, Hong Kong, December 16–19, 1994.
The first author was partially supported by the South African Foundation for Research Development. - Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2605-2614
- MSC (1991): Primary 45J05; Secondary 34G20
- DOI: https://doi.org/10.1090/S0002-9939-97-04149-X
- MathSciNet review: 1423341