THE EXISTANCE OF THE OPTIMUM SOLUTION FOR THE SYSTEM OF DIFFERENTIAL EQUATION IN HILBERT SPACE

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SOLTANI Z.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:3 | Issue:12 Page(s): 25-30

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Title

THE EXISTANCE OF THE OPTIMUM SOLUTION FOR THE SYSTEM OF DIFFERENTIAL EQUATION IN HILBERT SPACE

Author(s)

SOLTANI Z. | Issue Writer Certificate

Keywords

SYSTEM OF DIFFERENTIAL EQUATIONQ1

EVOLUTION CONTRACTION SYSTEMQ1

BEST PROXIMITY POINTSQ1

HILBERT SPACEQ1

Abstract

In this paper, we study the existence of the following optimum solution for the SYSTEM OF DIFFERENTIAL EQUATION (1) y’= Ay (t) + ¦(t, y (t)) t Î J = [0, T] y (t0)=y2, (2) y’= Ay (t) + g (t, y (t)) t Î J = [0, T] y (t0)= y1 in a HILBERT SPACEs in which ¦, g: J×H®H are single-valued maps, {A (t)} tÎJ is a family of linear operators in H and y1 y2 Î H.We prove the existence of the pair (x, y) such that x , y are the solution of differential equation (1) and (2) and ||x-y||=||y1-y2||The pair (x, y) is called the optimum solution of the SYSTEM OF DIFFERENTIAL EQUATION. Under suitable conditions on ¦, g and family of linear operators {A (t)}tÎJ. The results of the existence of the optimal solution are obtained by applying the BEST PROXIMITY POINTS for the integral equation to the differential equation system.

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APA: Copy

SOLTANI, Z.. (2018). THE EXISTANCE OF THE OPTIMUM SOLUTION FOR THE SYSTEM OF DIFFERENTIAL EQUATION IN HILBERT SPACE. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(12 ), 25-30. SID. https://sid.ir/paper/257370/en

Vancouver: Copy

SOLTANI Z.. THE EXISTANCE OF THE OPTIMUM SOLUTION FOR THE SYSTEM OF DIFFERENTIAL EQUATION IN HILBERT SPACE. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;3(12 ):25-30. Available from: https://sid.ir/paper/257370/en

IEEE: Copy

Z. SOLTANI, “THE EXISTANCE OF THE OPTIMUM SOLUTION FOR THE SYSTEM OF DIFFERENTIAL EQUATION IN HILBERT SPACE,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 12 , pp. 25–30, 2018, [Online]. Available: https://sid.ir/paper/257370/en

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