On the Existence of Solutions of Two Optimization Problems

Mariam Arabyan ()
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Mariam Arabyan: Yerevan State University

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 2, No 2, 305 pages

Abstract: Abstract In this paper, we prove the existence of solutions for the minimization problem of the shell weight for a given minimal frequency of the shell vibrations as well as for the maximization problem of the minimal frequency for a given shell weight. We consider an optimal control problem governed by an eigenvalue problem for a system of differential equations with variable coefficients. The form of the shell is considered as a control. Some of the coefficients are non-measurable. Earlier, we introduced certain special weighted functional spaces. By using these spaces, we establish the continuity of the considered minimal frequency functional and obtain the existence of solutions of both optimal control problems. At the end, we prove the Lipschitz continuity of the eigenvalue problem.

Keywords: Eigenvalues; Eigenfunctions; Continuous dependence; The shell of rotation; Weighted spaces; Non-measurable coefficients; Lipschitz continuity; 34B09; 49J15 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1266-9

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