Applications of the spectral radius to some integral equations

Mirosława Zima

Displaying similar documents to “Applications of the spectral radius to some integral equations”

On the local spectral radius in partially ordered Banach spaces

Mirosława Zima (1999)

Czechoslovak Mathematical Journal

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Remarks on existence of positive solutions of some integral equations

Jan Ligęza (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We study the existence of positive solutions of the integral equation $x (t) = μ \int_{0}^{1} k (t, s) f (s, x (s), x^{'} (s), ..., x^{(n - 1)} (s)) d s, n \geq 2$ in both $C^{n - 1} [0, 1]$ and $W^{n - 1, p} [0, 1]$ spaces, where $p \geq 1$ and $μ > 0$ . Throughout this paper $k$ is nonnegative but the nonlinearity $f$ may take negative values. The Krasnosielski fixed point theorem on cone is used.

On the joint spectral radius

Vladimír Müller (1997)

Annales Polonici Mathematici

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We prove the $_{p}$ -spectral radius formula for n-tuples of commuting Banach algebra elements

Spectral radius inequalities for positive commutators

Mirosława Zima (2014)

Czechoslovak Mathematical Journal

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We establish several inequalities for the spectral radius of a positive commutator of positive operators in a Banach space ordered by a normal and generating cone. The main purpose of this paper is to show that in order to prove the quasi-nilpotency of the commutator we do not have to impose any compactness condition on the operators under consideration. In this way we give a partial answer to the open problem posed in the paper by J. Bračič, R. Drnovšek, Y. B. Farforovskaya, E. L. Rabkin,...