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Extremal Solutions of a Class of Nonlinear Integro-Differential Equations in Banach spaces

Authors: Hong-Kun Xu and Juan J. Nieto
Journal: Proc. Amer. Math. Soc. 125 (1997), 2605-2614
MSC (1991): Primary 45J05; Secondary 34G20
MathSciNet review: 1423341
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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.

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Additional Information

Hong-Kun Xu
Affiliation: Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa

Juan J. Nieto
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain

Keywords: Periodic boundary value problem, first order nonlinear integro-differential equation, Green's function, monotone iterative technique, minimal and maximal solutions, normal cone, Banach space
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
Article copyright: © Copyright 1997 American Mathematical Society

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