Optimal Solution for the System of Differential Inclusion in Hilbert Space

Document Type : Original Scientific Paper


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


In this paper, we study the existence of the following optimal solution for the system of differential inclusion
y′ ∈ 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.


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