Noncompact‐type Krasnoselskii fixed‐point theorems and their applications |
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| Authors: | Tian Xiang Svetlin Georgiev Georgiev |
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| Affiliation: | 1. Institute for Mathematical Sciences, Renmin University of China, Beijing, China;2. Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria |
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| Abstract: | In this paper, we first establish some user‐friendly versions of fixed‐point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed‐point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed‐point theorem. Next, with these obtained fixed‐point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra‐type integral equations. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | transport equations fixed point theorems noncompact mappings measure of noncompactness contractions expansions integral equations difference equations |
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