        TY  - JOUR
T1  - The continuity of solution set of a multivalued equation and applications in control problem
AU  - Trı, Vo Viet
AU  - Thanh  Phong, Tran
PY  - 2021
DA  - September
DO  - 10.31197/atnaa.901582
JF  - Advances in the Theory of Nonlinear Analysis and its Application
JO  - ATNAA
PB  - Erdal KARAPINAR
WT  - DergiPark
SN  - 2587-2648
SP  - 330
EP  - 336
VL  - 5
IS  - 3
LA  - en
AB  - In this paper, we prove the existence, unbounded continuity of positive set for a  multivalued equation containing a parameter of the form $x \in A \circ F(\lambda,x)$ 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 }(t) +g(\lambda,t) f(u(t)) =0,\text{ }t\in (0,1) , \\ g(\lambda,t) \in F(\lambda,u(t)) \text{  a.e.  on } J\\u(0) =0, u( 1) =\sum_{i=1}^{m}\alpha_{i} u( \eta _{i})\end{array}\right. \label{Eq3.1}\end{equation}
KW  - multivalued operator
KW  - multivalued equation
KW  - fixed point index
KW  - control problem
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UR  - https://doi.org/10.31197/atnaa.901582
L1  - https://dergipark.org.tr/en/download/article-file/1656300
ER  -