Electron. J. Differential Equations, Vol. 2023 (2023), No. 07, pp. 123.
Existence and controllability for neutral partial differential inclusions nondenselly defined on a halfline
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
$$ \displaylines{
\frac{d}{dt}\mathcal{D}y_tA\mathcal{D}y_tLy_t \in F(t,y_t), \quad
\text{for a.e. }t \in J:=[0,\infty),\\
y_0=\phi \in C_E=C([r,0];E),\quad r>0,
}$$
and the controllability of the corresponding neutral inclusion
$$
\displaylines{
\frac{d}{dt}\mathcal{D}y_tA\mathcal{D}y_tLy_t \in F(t,y_t)+Bu(t),
\quad \text{for a.e. } t \in J,\\
y_0=\phi \in C_E,
}$$
on a halfline via the nonlinear alternative of LeraySchauder 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: HilleYosida 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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