Cite this article as:
Timashova E. V., Ivannikova . ., Shabrov S. 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. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 2, pp. 3-8. DOI: https://doi.org/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
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.
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