LOCALLY LIPSCHITZ COMPOSITION OPERATORS AND APPLICATIONS TO NONLINEAR INTEGRAL EQUATIONS

作者：Appell J^*; Guanda N; Lysakova Yu

来源：Journal of Integral Equations and Applications, 2013, 25(3): 321-339.

DOI：10.1216/JIE-2013-25-3-321

• Composition operator
• global Lipschitz condition
• local Lipschitz condition
• functions of bounded variation
• Holder continuous functions
• contraction mapping principle
• nonlinear integral equation

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%26apos;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.

• 出版日期2013