On the equivalence of variational problems. III
A note on the criteria of uniqueness of the solution of equation
A double complex related with a system of partial differential equations. II
Another approach to the classical calculus of variations. I
A double complex related with a system of partial differential equations. I
An application of inaccessible alephs
Inverse problem of the classical calculus of variations
On a theorem of J. Peetre
Another approach to the classical calculus of variations. II. Hamiltonian theory
Another approach to the classical calculus of variations. III
Boundary value problems for linear partial differential equation with constant coefficients. Homogeneous equation in the half plane
Boundary value problems for linear partial differential equation with constant coefficients. Non-homogeneous equation in the halfplane
O splynutí základních centrálních dispersí 3. a 4. druhu diferenciální rovnice
On formal theory of differential equations. II.
Corrections to the paper: “On formal theory of differential equations. II.”
On formal theory of differential equations. I.
From elementary algebra to Bäcklund transformations
On the equivalence of variational problems. II
Elements of general theory of infinitely prolonged underdetermined systems of ordinary differential equations are outlined and applied to the equivalence of one-dimensional constrained variational integrals. The relevant infinite-dimensional variant of Cartan’s moving frame method expressed in quite elementary terms proves to be surprisingly efficient in solution of particular equivalence problems, however, most of the principal questions of the general theory remains unanswered. New concepts of...
Solution of the inverse problem of the calculus of variations
Given a family of curves constituting the general solution of a system of ordinary differential equations, the natural question occurs whether the family is identical with the totality of all extremals of an appropriate variational problem. Assuming the regularity of the latter problem, effective approaches are available but they fail in the non-regular case. However, a rather unusual variant of the calculus of variations based on infinitely prolonged differential equations and systematic use of...
On formal theory of differential equations. III.
Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy...
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