Electron. J. Differential Equations, Vol. 2023 (2023), No. 07, pp. 1-23.

Existence and controllability for neutral partial differential inclusions nondenselly defined on a half-line

Nguyen Thi Van Anh, Bui Thi Hai Yen

Abstract:
In this article, we study the existence of the integral solution to the neutral functional differential inclusion $$ \displaylines{ \frac{d}{dt}\mathcal{D}y_t-A\mathcal{D}y_t-Ly_t \in F(t,y_t), \quad \text{for a.e. }t \in J:=[0,\infty),\\ y_0=\phi \in C_E=C([-r,0];E),\quad r>0, }$$ and the controllability of the corresponding neutral inclusion $$ \displaylines{ \frac{d}{dt}\mathcal{D}y_t-A\mathcal{D}y_t-Ly_t \in F(t,y_t)+Bu(t), \quad \text{for a.e. } t \in J,\\ y_0=\phi \in C_E, }$$ on a half-line via the nonlinear alternative of Leray-Schauder type for contractive multivalued mappings given by Frigon. We illustrate our results with applications to a neutral partial differential inclusion with diffusion, and to a neutral functional partial differential equation with obstacle constrains.

Submitted January 17, 2022. Published January 20, 2023.
Math Subject Classifications: 34G25, 34K35, 34K40, 93B05
Key Words: Hille-Yosida operators; neutral differential inclusions; multivalued maps; fixed point arguments; controllability.
DOI: https://doi.org/10.58997/ejde.2023.07

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Nguyen Thi Van Anh
Department of Mathematics
Hanoi National University of Education
No. 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
email: anhntv.ktt@hnue.edu.vn
Bui Thi Hai Yen
Department of Mathematics
Hoa Lu University
Ninh Nhat, Ninh Binh, Vietnam
email: bthyen.ktn@hluv.edu.vn

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