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Regulated solutions for nonlinear measure driven equations |
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| Affiliation: | 1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China;2. School of Mathematics and Statistics Science, Ludong University, Yantai 264025, PR China;1. College of Mathematics and Econometrics, Hunan University, 410082 Changsha, Hunan, PR China;2. School of Mathematical Sciences, Huaqiao University, 362021 Quanzhou, Fujian, PR China;3. Hunan Women’s University, 410004 Changsha, Hunan, PR China |
| Abstract: | We obtain the existence of regulated solutions for measure integral equations driven by a nondecreasing function, thus modeling a large class of hybrid systems (without any restriction on their Zeno behavior). By working with Kurzweil–Stieltjes integrals and making use of a measure of noncompactness, we are able to avoid Lipschitz-type assumptions. We finally present very useful particular cases and further applications of our result. |
| Keywords: | Measure differential equation Regulated solution Kurzweil–Stieltjes integral Measure of noncompactness |
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