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On the existence of oscillatory solutions in the Weisbuch-Salomon-Atlan model for the Belousov-Zhabotinskij reaction

Valter Šeda (1978)

Aplikace matematiky

The stability properties of solutions of the differential system which represents the considered model for the Belousov - Zhabotinskij reaction are studied in this paper. The existence of oscillatory solutions of this system is proved and a theorem on separation of zero-points of the components of such solutions is established. It is also shown that there exists a periodic solution.

On the number of limit cycles of a generalized Abel equation

Naeem Alkoumi, Pedro J. Torres (2011)

Czechoslovak Mathematical Journal

New results are proved on the maximum number of isolated T -periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.

On the Poincaré-Lyapunov constants and the Poincare series

Jaume Giné, Xavier Santallusia (2001)

Applicationes Mathematicae

For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial...

On the semilinear multi-valued flow under constraints and the periodic problem

Ralf Bader (2000)

Commentationes Mathematicae Universitatis Carolinae

* * In the paper we will be concerned with the topological structure of the set of solutions of the initial value problem of a semilinear multi-valued system on a closed and convex set. Assuming that the linear part of the system generates a C 0 -semigroup we show the R δ -structure of this set under certain natural boundary conditions. Using this result we obtain several criteria for the existence of periodic solutions for the semilinear system. As an application the problem of controlled heat transfer...

On the solution set of the nonconvex sweeping process

Andrea Gavioli (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We prove that the solutions of a sweeping process make up an R δ -set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.

On unbounded solutions for differential equations with mean curvature operator

Zuzana Došlá, Mauro Marini, Serena Matucci (2025)

Czechoslovak Mathematical Journal

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.

Currently displaying 301 – 320 of 587