Displaying similar documents to “Examples from the calculus of variations. II. A degenerate problem”

Examples from the calculus of variations. I. Nondegenerate problems

Jan Chrastina (2000)

Mathematica Bohemica

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The criteria of extremality for classical variational integrals depending on several functions of one independent variable and their derivatives of arbitrary orders for constrained, isoperimetrical, degenerate, degenerate constrained, and so on, cases are investigated by means of adapted Poincare-Cartan forms. Without ambitions on a noble generalizing theory, the main part of the article consists of simple illustrative examples within a somewhat naive point of view in order to obtain...

Killing's equations in dimension two and systems of finite type

Gerard Thompson (1999)

Mathematica Bohemica

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A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.

Note on simultaneous solutions of a system of Schröder's equations

Jan Čermák (1995)

Mathematica Bohemica

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We investigate simultaneous solutions of a system of Schroder's functional equations. Under certain assumptions these solutions are used in transformations of functional-differential equations the initial set of which consists of the initial point only.