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Existence and Uniqueness of Weak Solution for Nonlinear Weighted (p; q)-Laplacian System with Application on an Optimal Control Problem

Salah A. Khafagy (1), Eada. A. El-Zahrani (2) and Hassan M. Serag (3)

(1,3) Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt

Email address: (1) salahabdlnaby.211@azhar.edu.eg

Email address: (3) serragghm@yahoo.com

 

(2) Department of Mathematics, Faculty of Science, Damma University, Al-Damma, Saudia Arabia

Email address: eada11@hotmail.com

Doi : https://doi.org/10.47013/15.4.13

Cited by : Jordan J. Math & Stat., 15 (4A) (2022), 983 - 998

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Received on: Aug. 3, 2021;                                               Accepted on: Feb. 13, 2022

 Abstract. In this paper, we prove the existence and uniqueness results of weak solution for weighted (p, q)-Laplacian system with Dirichlet boundary condition.
The proof of the results is made by Browder theorem method. Also, the optimal control of the weighted (p, q)-Laplacian system will be study as an application.

Keywords: Weak solutions, p-Laplacian, optimal control.