Displaying similar documents to “Higher-order differential systems and a regularization operator”

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

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Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator ℓ ( y ) ≡ 1 w ( t ) ( r ( t ) y ) , t ∈ [ a , ∞ ) are established. These conditions are based on a recently proved relationship between spectral properties of ℓ and oscillation of a certain associated second order differential equation.

On special Riemannian 3 -manifolds with distinct constant Ricci eigenvalues

Oldřich Kowalski, Zdeněk Vlášek (1999)

Mathematica Bohemica

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The first author and F. Prufer gave an explicit classification of all Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying additional geometrical conditions. The aim of the present paper is to get the same classification under weaker geometrical conditions.

On one-sided estimates for row-finite systems of ordinary differential equations

Gerd Herzog (1999)

Mathematica Bohemica

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We prove an existence and uniqueness theorem for row-finite initial value problems. The right-hand side of the differential equation is supposed to satisfy a one-sided matrix Lipschitz condition with a quasimonotone row-finite matrix which has an at most countable spectrum.

On systems of linear algebraic equations in the Colombeau algebra

Jan Ligęza, Milan Tvrdý (1999)

Mathematica Bohemica

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From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra ℝ ¯ of generalized real numbers. It is worth mentioning that the algebra ℝ ¯ is not a field.