Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 07, pp. 1-23.

Title: Existence and controllability for neutral partial differential inclusions nondenselly defined on a half-line
       
Authors: Nguyen Thi Van Anh (Hanoi National Univ. of Education, Hanoi, Vietnam)
         Bui Thi Hai Yen (Hoa Lu Univ.,  Ninh Binh, Vietnam)
         
Abstract:
In this article, we study the existence of the integral solution to the neutral functional differential inclusion
$$\displaylines{
\frac{d}{dt}\mathcal{D}y_t-A\mathcal{D}y_t-Ly_t \in F(t,y_t), \quad
\text{for a.e. }t \in J:=[0,\infty),\cr
y_0=\phi \in C_E=C([-r,0];E),\quad r>0,
}$$
and the controllability of the corresponding neutral inclusion
$$\displaylines{ 
\frac{d}{dt}\mathcal{D}y_t-A\mathcal{D}y_t-Ly_t \in F(t,y_t)+Bu(t),
\quad  \text{for a.e. } t \in J,\cr
y_0=\phi \in C_E,
}$$
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.