The continuity of solution set of a multivalued equation and applications in control problem
| Autor: | Vo Viet Tri, Tran Thanh Phong |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Advances in the Theory of Nonlinear Analysis and its Applications, Vol 5, Iss 3, Pp 330-336 (2021) Volume: 5, Issue: 3 330-336 Advances in the Theory of Nonlinear Analysis and its Application |
| ISSN: | 2587-2648 |
| Popis: | 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} |
| Databáze: | OpenAIRE |
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