The continuity of solution set of a multivalued equation and applications in control problem

Authors : Tran THANH PHONG, Vo Viet TRI

Pages : 330-336

Doi:10.31197/atnaa.901582

View : 9 | Download : 4

Publication Date : 2021-09-30

Article Type : Research Paper

Abstract :In this paper, we prove the existence, unbounded continuity of positive set for a multivalued equation containing a parameter of the form $x \in A \circ Finsert ignore into journalissuearticles values(\lambda,x);$ and give applications in the control problem with multi-point boundary conditions and second order derivative operator \begin{equation} \left\{ \begin{array}{l} u^{\prime \prime }insert ignore into journalissuearticles values(t); +ginsert ignore into journalissuearticles values(\lambda,t); finsert ignore into journalissuearticles values(uinsert ignore into journalissuearticles values(t);); =0,\text{ }t\in insert ignore into journalissuearticles values(0,1); , \\ ginsert ignore into journalissuearticles values(\lambda,t); \in Finsert ignore into journalissuearticles values(\lambda,uinsert ignore into journalissuearticles values(t);); \text{ a.e. on } J \\ uinsert ignore into journalissuearticles values(0); =0, uinsert ignore into journalissuearticles values( 1); =\sum_{i=1}^{m}\alpha_{i} uinsert ignore into journalissuearticles values( \eta _{i}); \end{array} \right. \label{Eq3.1} \end{equation}
Keywords : multivalued operator, multivalued equation, fixed point index, control problem