Displaying similar documents to “Discrete spectra criteria for singular difference operators”

Higher-order differential systems and a regularization operator

Pavel Calábek (1999)

Mathematica Bohemica

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Sufficient conditions for the existence of solutions to boundary value problems with a Caratheodory right hand side for ordinary differential systems are established by means of continuous approximations.

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.

Linear Stieltjes integral equations in Banach spaces

Štefan Schwabik (1999)

Mathematica Bohemica

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Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces have been presented in []. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. []). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Here basic results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) are presented on the...

A second look on definition and equivalent norms of Sobolev spaces

Joachim Naumann, Christian G. Simader (1999)

Mathematica Bohemica

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Sobolev’s original definition of his spaces L m , p ( Ω ) is revisited. It only assumed that Ω ⊆ ℝ n is a domain. With elementary methods, essentially based on Poincare’s inequality for balls (or cubes), the existence of intermediate derivates of functions u ∈ L m , p ( Ω ) with respect to appropriate norms, and equivalence of these norms is proved.

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.

Comparison theorems for differential equations of neutral type

Miroslava Růžičková (1997)

Mathematica Bohemica

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We are interested in comparing the oscillatory and asymptotic properties of the equations L n [ x ( t ) - P ( t ) x ( g ( t ) ) ] + δ f ( t , x ( h ( t ) ) ) = 0 with those of the equations M n [ x ( t ) - P ( t ) x ( g ( t ) ) ] + δ Q ( t ) q ( x ( r ( t ) ) ) = 0 .