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Fixed point theorems for a class of nonlinear operators in Banach spaces and applications

✍ Scribed by Xiaoyan Zhang

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 237 KB
Volume: 69
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2007.05.040

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✦ Synopsis

In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of upper and lower solutions and compactness and continuity conditions. The results in this paper are applied to a class of abstract semilinear evolution equations with noncompact semigroup in Banach spaces and the initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces. The results obtained here improve and generalize many known results.

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