1. Existence of monotonic Lφ-solutions for quadratic Volterra functional-integral equations.
- Author
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Cichoń, Mieczysław and Metwali, Mohamed M. A.
- Subjects
- *
EXISTENCE theorems , *MONOTONIC functions , *QUADRATIC equations , *FUNCTIONAL integration , *INTEGRAL equations , *LEBESGUE measure - Abstract
We study the quadratic integral equation in the space of Orlicz space Eφ in the most important case when φ satisfies the D2-condition. Considered operators are not compact and then we use the technique of measure of noncompactness associated with the Darbo fixed point theorem to prove the existence of a monotonic, but discontinuous solution. Our present work allows to generalize both previously proved results for quadratic integral equations, as well as, that for classical equations. Due to different continuity properties of considered operators in Orlicz spaces, we distinguish different cases and we study the problem in the most important case - in such a way to cover all Lebesgue spaces Lp (p ≥ 1). [ABSTRACT FROM AUTHOR]
- Published
- 2015
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