Existence and compactness of solutions to impulsive differential equations with nonlocal conditions |
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| Authors: | Jung‐Chan Chang |
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| Affiliation: | Department of Applied Mathematics, I‐Shou University, Kaohsiung City, Taiwan |
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| Abstract: | The new type of nonlinear integral inequalities of Volterra–Fredholm type for discontinuous functions is investigated. Then, by using these inequalities and Schaefer fixed‐point theorem, we present new existence results for impulsive semilinear differential equations with nonlocal conditions. Moreover, the compactness of solution sets can be shown in some certain conditions. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | integral inequality fixed‐point theorem compact semigroup impulsive condition nonlocal condition |
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