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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.:
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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 1992, Volume 40, Pages 3–176 (Mi intd131)  

This article is cited in 9 scientific papers (total in 9 papers)

Variational principles for nonpotential operators

V. M. Filippov, V. M. Savchin, S. G. Shorokhov


Abstract: One presents numerous approaches for the construction of variational principles for equations with operators which, in general, are nonpotential. One considers separately linear and nonlinear ordinary differential equations, partial and integropartial differential equations. One constructs and investigates both extremal and stationary variational principles and one gives applications of these principles in theoretical physics and in analytic mechanics. A series of unsolved problems are indicated. The survey is intended for mathematicians, physicists, working in both theoretical and applied areas, as well as for graduate students of physics and mathematics.

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English version:
Journal of Mathematical Sciences, 1994, 68:3, 275–398

Bibliographic databases:

UDC: 517.972.5+517.972.7

Citation: V. M. Filippov, V. M. Savchin, S. G. Shorokhov, “Variational principles for nonpotential operators”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 40, VINITI, Moscow, 1992, 3–176; J. Math. Sci., 68:3 (1994), 275–398

Citation in format AMSBIB
\Bibitem{FilSavSho92}
\by V.~M.~Filippov, V.~M.~Savchin, S.~G.~Shorokhov
\paper Variational principles for nonpotential operators
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1992
\vol 40
\pages 3--176
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd131}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1270022}
\zmath{https://zbmath.org/?q=an:0766.49031|0835.58012}
\transl
\jour J. Math. Sci.
\yr 1994
\vol 68
\issue 3
\pages 275--398
\crossref{https://doi.org/10.1007/BF01252319}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. E. Tarasov, “Quantum dissipative systems. III. Definition and algebraic structure”, Theoret. and Math. Phys., 110:1 (1997), 57–67  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. M. Popov, “Inverse Problem of the Calculus of Variations for Systems of Differential-Difference Equations of Second Order”, Math. Notes, 72:5 (2002), 687–691  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. M. Savchin, S. A. Budochkina, “On the Existence of a Variational Principle for an Operator Equation with Second Derivative with Respect to “Time””, Math. Notes, 80:1 (2006), 83–90  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. M. V. Neshchadim, “Some questions concerning constructive methods in the theory of inverse problems”, J. Appl. Industr. Math., 3:2 (2009), 267–274  mathnet  crossref  mathscinet
    5. I. A. Kolesnikova, “Necessary and sufficient conditions for the existence of symmetry groups for systems of differential-difference equations with partial derivatives”, Journal of Mathematical Sciences, 180:6 (2012), 673–684  mathnet  crossref  mathscinet
    6. V. Zh. Sakbaev, “Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations”, Journal of Mathematical Sciences, 213:3 (2016), 287–459  mathnet  crossref  mathscinet
    7. V. M. Filippov, V. M. Savchin, S. A. Budochkina, “On the existence of variational principles for differential–difference evolution equations”, Proc. Steklov Inst. Math., 283 (2013), 20–34  mathnet  crossref  crossref  mathscinet  isi  elib
    8. V. M. Savchin, S. A. Budochkina, “On invariance of functionals and Euler–Lagrange equations corresponding to them”, Russian Math. (Iz. VUZ), 61:2 (2017), 49–54  mathnet  crossref  isi
    9. V. M. Savchin, S. A. Budochkina, “Li-dopustimye algebry, svyazannye s dinamicheskimi sistemami”, Sib. matem. zhurn., 60:3 (2019), 655–663  mathnet  crossref
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