A note on the fundamental matrix of variational equations in $\mathbb {R}^3$

Ladislav Adamec

Displaying similar documents to “A note on the fundamental matrix of variational equations in $ℝ^{3}$ ”

A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension

Ladislav Adamec (2005)

Applications of Mathematics

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In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.

A partial generalization of Diliberto’s theorem for certain DEs of higher dimension

Adamec, Ladislav

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On the invariant variational sequences in mechanics

Šeděnková, Jana

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Summary: The $r$ -th order variational sequence is the quotient sequence of the De Rham sequence on the $r$ th jet prolongation of a fibered manifold, factored through its contact subsequence.In this paper, the first order variational sequence on a fibered manifold with one-dimensional base is considered. A new representation of all quotient spaces as some spaces of (global) forms is given. The factorization procedure is based on a modification of the interior Euler operator, used in the theory...

Examples of bifurcation of periodic solutions to variational inequalities in $ℝ^{κ}$

Milan Kučera (2000)

Czechoslovak Mathematical Journal

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A bifurcation problem for variational inequalities $U (t) \in K, (\dot{U} (t) - B_{λ} U (t) - G (λ, U (t)), Z - U (t)) \geq 0 for all Z \in K, a.a. t \geq 0$ is studied, where $K$ is a closed convex cone in $ℝ^{κ}$ , $κ \geq 3$ , $B_{λ}$ is a $κ \times κ$ matrix, $G$ is a small perturbation, $λ$ a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.

Displaying similar documents to “A note on the fundamental matrix of variational equations in ℝ 3 ”

A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension

A partial generalization of Diliberto’s theorem for certain DEs of higher dimension

On the invariant variational sequences in mechanics

Examples of bifurcation of periodic solutions to variational inequalities in ℝ κ

Displaying similar documents to “A note on the fundamental matrix of variational equations in $ℝ^{3}$ ”

Examples of bifurcation of periodic solutions to variational inequalities in $ℝ^{κ}$