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On asymptotic decaying solutions for a class of second order differential equations

Serena Matucci (1999)

Archivum Mathematicum

The author considers the quasilinear differential equations r ( t ) ϕ ( x ' ) ' + q ( t ) f ( x ) = 0 , t a and r ( t ) ϕ ( x ' ) ' + F ( t , x ) = ± g ( t ) , t a . By means of topological tools there are established conditions ensuring the existence of nonnegative asymptotic decaying solutions of these equations.

On bounded nonoscillatory solutions of third-order nonlinear differential equations

Ivan Mojsej, Alena Tartaľová (2009)

Open Mathematics

This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. We give the necessary and sufficient conditions guaranteeing the existence of bounded nonoscillatory solutions. Sufficient conditions are proved via a topological approach based on the Banach fixed point theorem.

On certain properties of linear iterative equations

Jean-Claude Ndogmo, Fazal Mahomed (2014)

Open Mathematics

An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained,...

On certain singular third order eigenvalue problem

Michal Greguš, Michal Greguš, Jr. (2003)

Archivum Mathematicum

In this paper a singular third order eigenvalue problem is studied. The results of the paper complete the results given in the papers [3], [5].

On conditioning of Schur complements of H-TFETI clusters for 2D problems governed by Laplacian

Petr Vodstrčil, Jiří Bouchala, Marta Jarošová, Zdeněk Dostál (2017)

Applications of Mathematics

Bounds on the spectrum of the Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients in the analysis of many domain decomposition methods. Here we are interested in the analysis of floating clusters, i.e. subdomains without prescribed Dirichlet conditions that are decomposed into still smaller subdomains glued on primal level in some nodes and/or by some averages. We give the estimates of the regular condition number of the Schur complements...

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