Note on simultaneous solutions of a system of Schröder's equations

Jan Čermák

Displaying similar documents to “Note on simultaneous solutions of a system of Schröder's equations”

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 $\bar{ℝ}$ of generalized real numbers. It is worth mentioning that the algebra $\bar{ℝ}$ is not a field.

On condensing discrete dynamical systems

Valter Šeda (2000)

Mathematica Bohemica

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In the paper the fundamental properties of discrete dynamical systems generated by an $α$ -condensing mapping ( $α$ is the Kuratowski measure of noncompactness) are studied. The results extend and deepen those obtained by M. A. Krasnosel’skij and A. V. Lusnikov in []. They are also applied to study a mathematical model for spreading of an infectious disease investigated by P. Takac in [], [].

Examples from the calculus of variations. II. A degenerate problem

Jan Chrastina (2000)

Mathematica Bohemica

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Continuing the previous Part I, the degenerate first order variational integrals depending on two functions of one independent variable are investigated.

Killing's equations in dimension two and systems of finite type

Gerard Thompson (1999)

Mathematica Bohemica

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A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.

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 $𝔾_{L}^{n}$ of $n$ -vector valued functions which are regulated on the closed interval $[0, 1]$ (i.e. such that can have only discontinuities of the first kind in $[0, 1]$ ) and left-continuous in the corresponding open interval $(0, 1) .$ 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 $f \in 𝔾_{L}^{n}$ , the columns of the $n \times n$ -matrix valued function $A$ belong to $𝔾_{L}^{n}$ , the entries of $B (t, .)$ have a bounded variation...

Generalized boundary value problems with linear growth

Valter Šeda (1998)

Mathematica Bohemica

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It is shown that for a given system of linearly independent linear continuous functionals $l_{i} C^{n - 1} \to ℝ$ , $i = 1, \dots, n$ , the set of all $n$ -th order linear differential equations such that the Green function for the corresponding generalized boundary value problem (BVP for short) exists is open and dense in the space of all $n$ -th order linear differential equations. Then the generic properties of the set of all solutions to nonlinear BVP-s are investigated in the case when the nonlinearity in the differential equation...