On nonlinear multipoint conjugate value problem for feedback control systems in the cone

Nguyen Bich Huy; Nguyen Dang Quang; Vo Viet Tri

doi:10.3934/dcdss.2023126

Article Contents

2024, Volume 17, Issue 3: 1119-1132. Doi: 10.3934/dcdss.2023126

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On nonlinear multipoint conjugate value problem for feedback control systems in the cone

1.
Group of Analysis and Applied Mathematics, Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam
2.
Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam
3.
FPT University - Campus in Ho Chi Minh City, Vietnam

^*Corresponding author: Vo Viet Tri
^*Corresponding author: Vo Viet Tri

Received: April 2023

Revised: June 2023

Early access: June 21, 2023

Published online: June 21, 2023

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Abstract

We consider the nonlinear conjugate multi-point boundary value problem with feedback control that finds functions $ u $ and $ q $ satisfying

$ \begin{align*} & \mathcal Lu(t) = q(t)F[t,u(t),u'(t),..., u^{(m-1)}(t)],\,\, q(t) \in \Phi[t,u(t)],\,\,\, t\in I, \hfill \\ & u^{(j)}(t_i) = 0, \,\,\,\,\, 1\leq i \leq l,\,\,\,\, 0\leq j\leq k_i-1, \hfill \end{align*} $

where $ \mathcal L $ is a linear differential operator of order $ m $, $ I = [0,1] $, $ 0 = t_1<...<t_l = 1 $, $ 2\leq l\leq \sum_{i = 1}^lk_i = m $. By using the fixed point theory for multivalued operators we prove the existence of one or two nontrivial solutions of the problem.

Keywords:

Mathematics Subject Classification: 34A40, 34B10, 34B18, 35P30, 47B60, 47H10.

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References

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