Displaying similar documents to “Symmetries in connection preserving deformations.”

The moving frames for differential equations. II. Underdetermined and functional equations

Václav Tryhuk, Oldřich Dlouhý (2004)

Archivum Mathematicum

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Continuing the idea of Part I, we deal with more involved pseudogroup of transformations x ¯ = ϕ ( x ) , y ¯ = L ( x ) y , z ¯ = M ( x ) z , ... applied to the first order differential equations including the underdetermined case (i.e. the Monge equation y ' = f ( x , y , z , z ' ) ) and certain differential equations with deviation (if z = y ( ξ ( x ) ) is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction...

Solvability of a periodic type boundary value problem for first order scalar functional differential equations

Robert Hakl, Alexander Lomtatidze, Jiří Šremr (2004)

Archivum Mathematicum

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Nonimprovable sufficient conditions for the solvability and unique solvability of the problem u ' ( t ) = F ( u ) ( t ) , u ( a ) - λ u ( b ) = h ( u ) are established, where F : is a continuous operator satisfying the Carathèodory conditions, h : R is a continuous functional, and λ .