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On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

Wenjie Gao, Junyu Wang (1995)

Annales Polonici Mathematici

The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [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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