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

Electronic Journal of Differential Equations

article

Nguyen Thi Van Anh¹  Bui Thi Hai Yen² 

[1] Department of Mathematics Hanoi National University of Education No. 136 Xuan Thuy;Department of Mathematics Hoa Lu University Ninh Nhat

关键词: Hille-Yosida operators;    neutral differential inclusions;    multivalued maps;    fixed point arguments;    controllability;   

DOI  :  10.58997/ejde.2023.07

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

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 partialdifferential inclusion with diffusion, and to a neutral functional partial differential equation with obstacle constrains.

【 授权许可】

CC BY