Abstract
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.
Citation
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. https://doi.org/10.1216/JIE-2013-25-3-321
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