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

Year 2021, Volume: 5 Issue: 3, 330 - 336, 30.09.2021

Tran Thanh Phong Vo Viet Trı

https://doi.org/10.31197/atnaa.901582

Abstract

In this paper, we prove the existence, unbounded continuity of positive set for a multivalued equation containing a parameter of the form $x \in A \circ F(\lambda,x)$ 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}

Keywords

multivalued operator, multivalued equation, fixed point index, control problem

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