Open Access
FALL 2013 Locally Lipschitz composition operators and applica- tions to nonlinear integral equations
J. Appell, N. Guanda, Yu. Lysakova
J. Integral Equations Applications 25(3): 321-339 (FALL 2013). DOI: 10.1216/JIE-2013-25-3-321


It is well known that imposing a global Lipschitz condition on nonlinear composition operators leads to a strong degeneracy phenomenon in many function spaces. In contrast to this, we show that a local version of Banach's contraction mapping principle is less restrictive and applies to a large variety of nonlinear problems. We illustrate this by means of applications to nonlinear integral equations with bounded or weakly singular kernels.


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J. Appell. N. Guanda. Yu. Lysakova. "Locally Lipschitz composition operators and applica- tions to nonlinear integral equations." J. Integral Equations Applications 25 (3) 321 - 339, FALL 2013.


Published: FALL 2013
First available in Project Euclid: 16 December 2013

zbMATH: 1298.47068
MathSciNet: MR3161616
Digital Object Identifier: 10.1216/JIE-2013-25-3-321

Primary: 47H30
Secondary: 26A16 , 26A45 , 45G05 , 45G10

Keywords: Composition operator , contraction mapping principle , Functions of bounded variation , global Lipschitz condition , Hölder continuous functions , local Lipschitz condition , nonlinear integral equation

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

Vol.25 • No. 3 • FALL 2013
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