Integral equations, L^p-forcing, remarkable resolvent: Liapunov functionals

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• 作者：T.A. Burton
• 关键词：Integral equations ; Resolvents ; Liapunov functionals
• 刊名：Nonlinear Analysis
• 出版年：2008
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：1 January 2008
• 卷：68
• 期：1
• 页码：35-46
• 文件大小：232 K

摘要

In this paper we study an integral equation of the form 175> with resolvent R(t,s) and variation-of-parameters formula eba4032">175>. We give a variety of conditions under which the mapping maps a vector space containing unbounded functions into an L^p space. It is known from the ideal theory of Ritt that R(t,s) is arbitrarily complicated. Thus, it is widely supposed that this integral is also extremely complicated. In fact, it is not. That integral can be a very close approximation to even when is unbounded. These unbounded functions are essentially harmless perturbations.