An abstract impulsive second-order functional-differential Cauchy problem with nonlocal conditions. (English) Zbl 1471.34142
Pinelas, Sandra (ed.) et al., Differential and difference equations with applications. Selected papers based on the presentations at the fourth international conference, ICDDEA 2019, Lisbon, Portugal, July 1–5, 2019. Cham: Springer. Springer Proc. Math. Stat. 333, 733-746 (2020).
Of concern is a nonlocal Cauchy problem for a semilinear impulsive second-order functional differential equation in a Banach space. The authors obtain sufficient conditions for the existence, uniqueness and continuous dependence on data of classical and mild solutions. The approach relies on the theory of strongly continuous cosine families of linear operators, and the contraction mapping theorem. The paper complements earlier studies of nonlocal problems by Akca and some of the coauthors.
For the entire collection see [Zbl 1445.34003].
For the entire collection see [Zbl 1445.34003].
Reviewer: Sergiu Aizicovici (Verona)
MSC:
| 34K30 | Functional-differential equations in abstract spaces |
| 34K45 | Functional-differential equations with impulses |
| 34K10 | Boundary value problems for functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
References:
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