Institute of Mathematics AS CR, v. v. i.
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On unbounded solutions for differential equations with mean curvature operator
No full textsummary:We present necessary and sufficient conditions for the existence of unbounded increasing solutions to ordinary differential equations with mean curvature operator. The results illustrate the asymptotic proximity of such solutions with those of an auxiliary linear equation on the threshold of oscillation. A new oscillation criterion for equations with mean curvature operator, extending Leighton criterion for linear Sturm-Liouville equation, is also derived
Positive periodic solutions to super-linear second-order ODEs
No full textsummary:We study the existence and uniqueness of a positive solution to the problem with a super-linear nonlinearity and a nontrivial forcing term . To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case
Boundary value problems with bounded -Laplacian and nonlocal conditions of integral type
No full textsummary:We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded -Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals
Linearization technique for oscillation of perturbed half-linear differential equations
Full text linksummary:It is shown that oscillation of perturbed second order half-linear differential equations can be derived from oscillation of second order linear differential equations associated with modified Riccati equations. In the main result of the present paper, some of technical assumptions in the known results of this type are removed
A stabilized formulation for the mortar method with non-linear contact constraints
No full textsummary:The mortar method is a powerful technique to enforce constraints between non-conforming discretizations by introducing a set of Lagrange multipliers on the connecting interface. Usually, the multipliers are not obtained explicitly because they can be eliminated with the aid of the so-called mortar interpolation operator. However, their explicit computation becomes essential when the contact constraint is governed by some non-linear law, and in this situation it is necessary to guarantee that discrete spaces of the primary variables and multipliers are inf-sup stable. In this work, we investigate the issue of inf-sup stability when using various families of piecewise linear and piecewise constant multipliers. The focus is on the role of the mesh resolution and the enforcement of boundary conditions, which are important factors in practical applications. Then, we develop a stabilized formulation for piecewise-constant multipliers inspired by the framework of minimal stabilization. The effectiveness of the proposed approach is demonstrated through numerical benchmarks and examples
The least squares solution of inconsistent discretized elliptic problems using the FETI method
No full textsummary:The variants of FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established, massively parallel algorithms for solving huge linear systems arising from the discretization of elliptic partial differential equations. Here, we adapt the FETI method for solving the large least squares problems associated with inconsistent systems of linear equations arising from the discretization of elliptic partial differential equations. We briefly review the symmetric least squares problems and the FETI method, explain how FETI can find the least squares solution, prove the optimal rate of convergence, and present the results of numerical experiments demonstrating the efficiency of the proposed method in solving the least squares problem defined by the Poisson equation with inconsistent Neumann conditions
On a few questions about character codegrees
No full textsummary:Let be a finite group and be a character of . We define the codegree of to be . We study a few questions raised by Qian about character codegrees
Frankl's Conjecture
No full textsummary:V článku se seznámíme s Franklovou hypotézou, která říká, že všechny konečné systémy množin uzavřené na sjednocení obsahují prvek, který patří alespoň do poloviny všech množin v systému. Rozebereme předpoklady hypotézy, základní poznatky, ekvivalentní formulace, vybrané známé částečné výsledky a výsledky týkající se malých systémů množin
Some remarks on plectic motivic spaces and spectra
No full textsummary:We formulate a motivic homotopy theory version of the plectic conjecture of J. Nekovář and A. J. Scholl and give some initial discussion of it