THE THEOREM OF THE RESOLUTION OF THE INVERSE PROBLEM OF VARIATION CALCULUS FOR THE ORDINARY DIFFERENTIAL EQUATIONS OF THE SIXTH ORDER
Authors:
Type:
Article
Pages:
from 90
to 0
Status:
Published
Received:
29.08.2014
Accepted:
03.10.2014
Published:
03.10.2014
Language:
Russian
Keywords:
the differential equations, the inverse problem of variation calculus, functional, Frechet differential
Abstract (English):
Necessary and sufficient conditions are obtained for the solvability of the inverse problem of the calculus of variations for ordinary differential equation of the sixth order. As a consequence of this result, we obtain necessary and sufficient conditions for the solvability of inverse problems of the variation calculus for the ordinary differential equations of the fourth and the second order, considered in [1].
Necessary and sufficient conditions are obtained for the solvability of the inverse problem of the calculus of variations for ordinary differential equation of the sixth order. As a consequence of this result, we obtain necessary and sufficient conditions for the solvability of inverse problems of the variation calculus for the ordinary differential equations of the fourth and the second order, considered in [1].
Keywords:
the differential equations, the inverse problem of variation calculus, functional, Frechet differential
the differential equations, the inverse problem of variation calculus, functional, Frechet differential
1. Zadorozhniy V. G. Differentsial´nye uravneniya s variatsionnymi proizvodnymi. Voronezh, VorGU, 2000.
2. Zadorozhniy V. G., Korchagina E. V. Usloviya razreshimosti obratnoy zadachi variatsionnogo ischisleniya dlya obyknovennogo differentsial´nogo uravneniya shestogo poryadka. Trudy molodykh uchenykh 2/2000, VGU, 2001. -s.48-61
