The continuity of solution set of a multi-point boundary problem with a control system
- Authors
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- Keywords:
- Multi-valued, Fixed point index, Feedback control, Multi-point boundary
- Abstract
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In this paper, we prove the unbounded continuity of the positive set of the inclusion \(x\in A\circ T(\lambda, x)\) and apply it to the problem that finds \((\lambda, u)\) satisfying
\begin{equation}
\left\{
\begin{array}{l}
D^{2 }u(t) +q(\lambda,t) f(t,u(t)) =0,\text{ }t\in (0,1) , \\
q(\lambda,t) \in F(\lambda,u(t)) \text{ a.e. } t\in [0,1]\\
u(0)=0\,\, ({\rm resp., }\, Du(0) =0), u( 1) =\sum_{j=1}^{m}\gamma_{j} u( \eta _{j}).
\end{array}
\right. \label{Eq0.1}
\end{equation}
Here, \(D^n\) is the derivative of n order \((D\equiv D^1)\). To obtain results, we use topological degree theories and the monotone lower evaluation for multivalued mapping in the infinite neighborhood of \(\lambda\). - References
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- Published
- 28-03-2025
- Issue
- Vol. 1 No. 1 (2023)
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- Research Article
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