Electron. J. Differential Equations, Vol. 2025 (2025), No. 118, pp. 1-13.

Topological properties of the solution set and T-controllability for second-order neutral evolution equations with delay

Tiantian Wang, Hongxia Fan

Abstract:
In this article we study the topological properties of the mild solution set and T-controllability for a class of second-order neutral evolution equations with finite delay. Firstly, we establish that the set of mild solution is nonempty and compact, via Darbo-Sadovskii's fixed point theorem with sufficient conditions provided to guarantee its \(R_{\delta}\)-property. Secondly, we show the trajectory-controllability of the equation, under an invertibility assumption on the control operator. Finally, with an example, we illustrate the applicability of the abstract results.

Submitted July 9, 2025. Published December 18, 2025
Math Subject Classifications: 93B05, 47J35, 93C10.
Key Words: R-delta-set; topological properties; trajectory-controllability; neutral evolution equations.
DOI: 10.58997/ejde.2025.118

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Tiantian Wang
School of Mathematics and Physics
Lanzhou Jiaotong University
Lanzhou, Gansu 730070, China
email: wtt_cassie@163.com
Hongxia Fan
School of Mathematics and Physics
Lanzhou Jiaotong University
Lanzhou, Gansu 730070, China
email: ffls0217@126.com

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