Differential Game with Integral Constraints in a Hilbert Space

Bilyaminu Muhammad and Hassan Abdullahi
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Bilyaminu Muhammad: Department of Mathematics, Federal College of Education (Technical), Gusau Zamfara State
Hassan Abdullahi: Department of Mathematics, Zamfara State University, Talata Mafara, Zamfara State

International Journal of Research and Innovation in Applied Science, 2025, vol. 10, issue 5, 155-159

Abstract: We study a pursuit differential game problem involving one pursuer and one evader in a Hilbert space. The motion of the pursuer is governed by first-order differential equations, while that of the evader is described by a second-order differential equation. The control functions of the pursuer and the evader are subject to integral constraints. The pursuit is considered completed if the equality y(θ)=x(θ) is achieved. We formulate and prove two theorems that provide sufficient conditions for the completion of pursuit at a given time.

Date: 2025
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