Existence and controllability for neutral partial differential inclusions nondenselly defined on a half-line
DOI:
https://doi.org/10.58997/ejde.2023.07Abstract
In this article, we study the existence of the integral solution to the neutral functional differential inclusion$${\frac{d}{dt}\mathcal{D}y_t-A\mathcal{D}y_t-Ly_t \in F(t,y_t), \quad\text{for a.e. }t \in J:=[0,\infty),\\ y_0=\phi \in C_E=C([-r,0];E),\quad r>0,}$$and the controllability of the corresponding neutral inclusion $${\frac{d}{dt}\mathcal{D}y_t-A\mathcal{D}y_t-Ly_t \in F(t,y_t)+Bu(t),\quad \text{for a.e. } t \in J,\\ y_0=\phi \in C_E,}$$ 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.
For more information see https://ejde.math.txstate.edu/Volumes/2023/07/abstr.html
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