Equivalence and symmetries of first order differential equations

V. Tryhuk

Displaying similar documents to “Equivalence and symmetries of first order differential equations”

The moving frames for differential equations. I. The change of independent variable

Václav Tryhuk, Oldřich Dlouhý (2003)

Archivum Mathematicum

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The article concerns the symmetries of differential equations with short digressions to the underdetermined case and the relevant differential equations with delay. It may be regarded as an introduction into the method of moving frames relieved of the geometrical aspects: the stress is made on the technique of calculations employing only the most fundamental properties of differential forms. The present Part I is devoted to a single ordinary differential equation subjected to the change...

Characterization of several classes of second-order ODEs by using differential invariants.

Martín del Rey, A., Muñoz Masqué, J. (2005)

International Journal of Mathematics and Mathematical Sciences

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Blow-up solutions of the self-dual Chern–Simons–Higgs vortex equation

Kwangseok Choe, Namkwon Kim (2008)

Annales de l'I.H.P. Analyse non linéaire

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Spectrum of the weighted Laplace operator in unbounded domains

Alexey Filinovskiy (2011)

Mathematica Bohemica

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We investigate the spectral properties of the differential operator $- r^{s} Δ$ , $s \geq 0$ with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm ${∥ u ∥}_{L_{2, s} (Ω)}^{2} = \int_{Ω} r^{- s} {| u |}^{2} d x$ , we study the structure of the spectrum with respect to the parameter $s$ . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.