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

[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.

[学科分类] 数学（综合）

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