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Existence, compactness, and connectedness of solution sets to nonlocal and impulsive Cauchy problems
Author(s) -
Chang JungChan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6139
Subject(s) - mathematics , compact space , social connectedness , initial value problem , cauchy problem , mathematical analysis , cauchy distribution , pure mathematics , psychology , psychotherapist
In this paper, by using some well‐known inequalities and Schaefer fixed point theorem, we show existence results for impulsive Cauchy problems with nonlocal conditions. The compactness of solution sets can be shown in some certain conditions. Moreover, connectedness of solution sets to impulsive Cauchy problems is shown.