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 with those of the equations
Displaying similar documents to “Spectral properties of fourth order differential operators”
Comparison theorems for differential equations of neutral type
On special Riemannian -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.
Linear integral equations in the space of regulated functions
Milan Tvrdý (1998)
Mathematica Bohemica
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n this paper we investigate systems of linear integral equations in the space of -vector valued functions which are regulated on the closed interval (i.e. such that can have only discontinuities of the first kind in ) and left-continuous in the corresponding open interval In particular, we are interested in systems of the form x(t) - A(t)x(0) - 01B(t,s)[d x(s)] = f(t), where , the columns of the -matrix valued function belong to , the entries of have a bounded variation...
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 of generalized real numbers. It is worth mentioning that the algebra is not a field.
Remarks on generalized solutions of ordinary linear differential equations in the Colombeau algebra
Jan Ligęza (1998)
Mathematica Bohemica
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In this paper first order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in , where denotes the Colombeau algebra.
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.