Optimal Solution for the System of Differential Inclusion in Hilbert Space
نویسندگان
1 Department of Pure Mathematics, University of Kashan, Kashan, 87317-53153, I. R. Iran
2 Basic Science Group, Golpayegan College of Engineering, Isfahan University of Technology, Golpayegan, 87717-67498, Iran
doi
10.22052/mir.2021.243050.1303چکیده
In this paper, we study the existence of the following optimal solution for the system of differential inclusiony′ ∈ Φ(t,y(t)) a.e. t ∈ I = [t0,b] and y(t0) = u2,y′ ∈ Ψ(t,y(t)) a.e. t ∈ I = [t0,b] and y(t0) = u1.in a Hilbert space, where Φ and Ψ are multivalued maps. Our existence result is obtained via selection technique and the best proximity point methods reducing the problem to a differential inclusion.
