Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems
نویسندگان
چکیده
منابع مشابه
Nonlocal Impulsive Cauchy Problems for Evolution Equations
Of concern is the existence of solutions to nonlocal impulsive Cauchy problems for evolution equations. Combining the techniques of operator semigroups, approximate solutions, noncompact measures and the fixed point theory, new existence theorems are obtained, which generalize and improve some previous results since neither the Lipschitz continuity nor compactness assumption on the impulsive fu...
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and Applied Analysis 3 Definition 2.1. The functions f and g are said to be L2-Carathéodory if 1 f t, x and g t, x are measurable in t and continuous in the second variable a.e. t ∈ J , 2 for each positive constant q, there exists a square integrable function hq : J → R such that ∥ ∥f t, u ∥ ∥ ∨ ∥g t, u ∥ ≤ hq t , ‖u‖ ≤ q, a.e. t ∈ J. 2.2 Motivated by 1, 7 , let us start by defining what we mea...
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ژورنال
عنوان ژورنال: Journal of Mathematics
سال: 2020
ISSN: 2314-4785,2314-4629
DOI: 10.1155/2020/5729128