Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Timashova E. V., Shabrov S. A., Ivannikova T. A. 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. Sarat. Univ. Math. Mech. Inform., 2013, vol. 13, iss. 2, pp. 3-8. DOI: 10.18500/1816-9791-2013-13-2-1-3-8

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
27.02.2013
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Russian
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UDC: 
517
DOI: 
10.18500/1816-9791-2013-13-2-1-3-8

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

Autors: 
Timashova Evgeniya Vladimirovna, Voronezh State University, Russia
Shabrov Sergey Aleksandrovich, Voronezh State University, Russia
Ivannikova Tat'yana Aleksandrovna, Voronezh State University, Russia
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. 

References: 
  1. Pokornyi Yu. V., Bakhtina Zh. I., Zvereva M. B., Shabrov S. A. Ostsilliatsionnyi metod Shturma v spektral’nykh zadach [Sturm oscillation method in spectral problems]. Moscow, Fizmatlit, 2009, 192 p. (in Russian).
  2. Shabrov S. A. On a necessary condition of at least one quadratic functional with an integral Stieltjes. Izv. Sarat. Univ. N. S. Ser. Math. Mech. Inform., 2012, vol. 12, iss. 1. pp. 52–55 (in Russian).
  3. Shabrov S. A. O μ-reguliarizatsii funktsii s konechnym izmeneniem [About μ-regularization of function of finite variation] Sb. statei aspirantov i studentov matematicheskogo fakul’teta VGU. Voronezh, 1999, pp. 166–169 (in Russian).
  4. Pokornyi Yu. V. The Stieltjes integral and derivatives with respect to the measure in ordinary differential equations. Dokl. Math., 1999, vol. 59, no. 1, pp. 34–37.
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