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This article is cited in 4 scientific papers (total in 4 papers)
Mathematics
On necessary conditions for a minimum of a quadratic functional with a Stieltjes integral and zero coefficient of the highest derivative on the part of the interval
T. A. Ivannikova, E. V. Timashova, S. A. Shabrov Voronezh State University, Russia, 394006, Voronezh, Universitetskaya pl., 1
Abstract:
In this paper we obtain a necessary condition for an extremum of a quadratic functional with a Stieltjes integral in the case where the coefficient of the highest derivative may vanish on a part of the interval. It is shown that the resulting mathematical model has the property of non-degeneracy. It is proved that a Variable boundary problem that arises as a necessary condition for an extremum is an “intermediate” position between the boundary value problems of fourth- and second-order – the solution space has dimension three.
Key words:
functional, a necessary condition, Stieltjes integral, derivative on the measure.
Citation:
T. A. Ivannikova, E. V. Timashova, S. A. Shabrov, “On necessary conditions for a minimum of a quadratic functional with a Stieltjes integral and zero coefficient of the highest derivative on the part of the interval”, Izv. Saratov Univ. Math. Mech. Inform., 13:2(1) (2013), 3–8
Linking options:
https://www.mathnet.ru/eng/isu389 https://www.mathnet.ru/eng/isu/v13/i3/p3
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