EUDML

Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.

Bifurcation of periodic solutions to variational inequalities in $ℝ^{κ}$ based on Alexander-Yorke theorem

Milan Kučera — 1999

Czechoslovak Mathematical Journal

Variational inequalities $U (t) \in K, (\dot{U} (t) - B_{λ} U (t) - G (λ, U (t)), Z - U (t)) \geq 0 for all Z \in K, a.a. t \in [0, T)$ are studied, where $K$ is a closed convex cone in $ℝ^{κ}$ , $κ \geq 3$ , $B_{λ}$ is a $κ \times κ$ matrix, $G$ is a small perturbation, $λ$ a real parameter. The assumptions guaranteeing a Hopf bifurcation at some $λ_{0}$ for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some $λ_{I} \neq λ_{0}$ . Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at $λ_{0}$ constructed...

Examples of bifurcation of periodic solutions to variational inequalities in $ℝ^{κ}$

Milan Kučera — 2000

Czechoslovak Mathematical Journal

A bifurcation problem for variational inequalities $U (t) \in K, (\dot{U} (t) - B_{λ} U (t) - G (λ, U (t)), Z - U (t)) \geq 0 for all Z \in K, a.a. t \geq 0$ is studied, where $K$ is a closed convex cone in $ℝ^{κ}$ , $κ \geq 3$ , $B_{λ}$ is a $κ \times κ$ matrix, $G$ is a small perturbation, $λ$ a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.

A new method for the obtaining of eigenvalues of variational inequalities of the special type (Preliminary communication)

Milan Kučera — 1977

Commentationes Mathematicae Universitatis Carolinae

A global continuation theorem for obtaining eigenvalues and bifurcation points

Milan Kučera — 1988

Czechoslovak Mathematical Journal

A new method for obtaining eigenvalues of variational inequalities based on bifurcation theory

Milan Kučera — 1979

Časopis pro pěstování matematiky

A new method for obtaining eigenvalues of variational inequalities. Branches of eigenvalues of the equation with the penalty in a special case

Milan Kučera — 1979

Časopis pro pěstování matematiky

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Stability and bifurcation problems for reaction-diffusion systems with unilateral conditions

Bifurcation problems for variational inequalities

A new method for obtaining eigenvalues of variational inequalities: operators with multiple eigenvalues

Book Reviews. EQUADIFF IV. Proceedings

Book review. Fučík, S., Nečas, J., Souček, J., Souček, V.: Spectral Analysis of Nonlinear Operators

Bifurcation points of variational inequalities

Fredholm alternative for nonlinear operators

Hausdorff measures of the set of critical values of functions of the class $C^{k, λ}$

Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities

Bifurcation of periodic solutions to variational inequalities in $ℝ^{κ}$ based on Alexander-Yorke theorem

Examples of bifurcation of periodic solutions to variational inequalities in $ℝ^{κ}$

A new method for the obtaining of eigenvalues of variational inequalities of the special type (Preliminary communication)

A global continuation theorem for obtaining eigenvalues and bifurcation points

A new method for obtaining eigenvalues of variational inequalities based on bifurcation theory

A new method for obtaining eigenvalues of variational inequalities. Branches of eigenvalues of the equation with the penalty in a special case

Perspektivy integrované optiky

Perturbations of variational inequalities and rate of convergence of solutions

Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions

Destabilizing effect of unilateral conditions in reaction-diffusion systems

Hopf bifurcation and ordinary differential inequalities