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⇱ Jan Eisner - Independent Researcher

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Tato stránka byla vytvořena v rámci univerzitního projektu ,, Vývoj slovanské archeologie a její významní představitelé"  z cílem přiblížit osobnost a dílo předního  českého  archeologa, zakladatele odborné archeologie na Slovensku, akademika, univ. prof. PhDr. Jan Eisner dr. h. c. (24. 4.1885 Dolní Bradlo - 2. 5. 1967 Praha)
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This site was created as part of a university project ,,Development of Slavic archeology and its prominent leaders", the aim of the person and work of prominent Czech archaeologist, founder of scientific archeology in the Slovak Republic, academic, univ. prof. PhDr. Jan Eisner dr.h.c. (24. 4.1885 Dolni Bradlo - 2. 5. 1967 Prague)
Address: Prague, Czech republic
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Archaeology Transcarpathia - Literature, sources by Jan Eisner

Odtlačok zo Sborníka Muzeálnej slovenskej spoločnosti, roč. XXVI, 1932, seš. 1- 4 * The fingerpri... more Odtlačok zo Sborníka Muzeálnej slovenskej spoločnosti, roč. XXVI, 1932, seš. 1- 4
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The fingerprint of Proceedings Muzeum Slovak society, Vol. XXVI, 1932, you are. 1-4
Odtlačok zo Sborníka Muzeálnej slovenskej spoločnosti, roč. XXVII-XXVIII, 1933-1934, seš. 1-8 * T... more Odtlačok zo Sborníka Muzeálnej slovenskej spoločnosti, roč. XXVII-XXVIII, 1933-1934, seš. 1-8
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The fingerprint of Proceedings museum Slovak society, Vol. XXVII-XXVIII, 1933-1934, you are. 1-8

Papers by Jan Eisner

Spatial patterning in reaction-diffusion systems with nonstandard boundary conditions
Hopf bifurcation and ordinary differential inequalities
Czechoslovak Mathematical Journal
Smooth bifurcation for an obstacle problem
Differential and Integral Equations
The existence of smooth families of solutions bifurcating from the trivial solution for a two-par... more The existence of smooth families of solutions bifurcating from the trivial solution for a two-parameter bifurcation problem for a class of variational inequalities is proved. As an example, a model of an elastic beam compressed by a force $\lambda$ and supported by a unilateral connected fixed obstacle at the height $h$ is studied. In the language of this example, we show that nontrivial solutions touching the obstacle on connected intervals bifurcate from the trivial solution and form smooth families parametrized by $\lambda$ and $h$. In particular, the corresponding contact intervals depend smoothly on $\lambda$ and $h$.
Smooth bifurcation for a Signorini problem on a rectangle
Mathematica Bohemica
We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundary con... more We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. We describe smooth branches of smooth nontrivial solutions bifurcating from the trivial solution branch in eigenvalues of the linearized problem. In particular, the contact sets of these nontrivial solutions are intervals which change smoothly along the branch. The main tools of the proof are first a certain local equivalence of the unilateral BVP to a system consisting of a corresponding classical BVP and of two scalar equations (which determine the ends of the contact intervals), and secondly an application of the classical Crandall-Rabinowitz type local bifurcation techniques (scaling and application of the Implicit Function Theorem) to that system.
Journal of Mathematical Analysis and Applications, 2005
We consider a class of variational inequalities with a multidimensional bifurcation parameter und... more We consider a class of variational inequalities with a multidimensional bifurcation parameter under assumptions guaranteeing the existence of smooth families of nontrivial solutions bifurcating from the set of trivial solutions. The direction of bifurcation is shown in a neighborhood of bifurcation points of a certain type. In the case of potential operators, also the stability and instability of bifurcating solutions and of the trivial solution is described in the sense of minima of the potential. In particular, an exchange of stability is observed.
Bifurcation Direction and Exchange of Stability for an Elliptic Unilateral BVP
More Progresses in Analysis - Proceedings of the 5th International ISAAC Congress, 2009
Direction and stability of bifurcating solutions for a Signorini problem
Nonlinear Analysis: Theory, Methods & Applications, 2015
ABSTRACT The equation Δu+λu+g(λ,u)u=0Δu+λu+g(λ,u)u=0 is considered in a bounded domain in R2R2 wi... more ABSTRACT The equation Δu+λu+g(λ,u)u=0Δu+λu+g(λ,u)u=0 is considered in a bounded domain in R2R2 with a Signorini condition on a straight part of the boundary and with mixed boundary conditions on the rest of the boundary. It is assumed that g(λ,0)=0g(λ,0)=0 for λ∈Rλ∈R, λλ is a bifurcation parameter. A given eigenvalue of the linearized equation with the same boundary conditions is considered. A smooth local bifurcation branch of non-trivial solutions emanating at λ0λ0 from trivial solutions is studied. We show that to know a direction of the bifurcating branch it is sufficient to determine the sign of a simple expression involving the corresponding eigenfunction u0u0. In the case when λ0λ0 is the first eigenvalue and the branch goes to the right, we show that the bifurcating solutions are asymptotically stable in W1,2W1,2-norm. The stability of the trivial solution is also studied and an exchange of stability is obtained.
Bifurcation of Solutions to Reaction-Diffusion Systems with Jumping Nonlinearities
Applied Nonlinear Analysis, 2002
ABSTRACT
Theoretical Population Biology, 2003
In the previous two articles ( Theor. Popul. Biol. 49 (1996) 265-290; 55 (1999) 111-126), the pop... more In the previous two articles ( Theor. Popul. Biol. 49 (1996) 265-290; 55 (1999) 111-126), the population dynamics resulting from a two-prey-one-predator system with adaptive predators was studied. In these articles, predators followed the predictions of optimal foraging theory. Analysis of that system was hindered by the incorporation of the logistic description of prey growth. In particular, because prey self-regulation dependence is a strong stabilizing mechanism, the effects of optimal foraging could not be easily separated from the effects of bottom-up control of prey growth on species coexistence. In this article, we analyze two models. The first model assumes the exponential growth of both prey types while the second model assumes the exponential growth of the preferred prey type and the logistic growth of the alternative prey type. This permits the effect of adaptive foraging on two-preypredator food webs to be addressed. We show that optimal foraging reduces apparent competition between the two prey types, promotes species coexistence, and leads to multiple attractors. r
Theoretical Population Biology, 2006
This article analyzes the classical 2-resource-1-consumer apparent competition community module w... more This article analyzes the classical 2-resource-1-consumer apparent competition community module with the Holling type II functional response. Two types of resource regulation (top-down vs. combined top-down and bottom-up) and two types of consumer behaviors (inflexible consumers with fixed preferences for resources vs. adaptive consumers) are considered. When resources grow exponentially and consumers are inflexible foragers, one resource is always outcompeted due to strong apparent competition. Density dependent resource growth relaxes apparent competition so that resources can coexist. As multiple attractors (either equilibria or limit cycles) coexist, population dynamics and community composition depend on initial population densities. Population dynamics change dramatically when consumers forage adaptively. In this case, the results both for top-down, and combined top-down and bottom-up regulation are similar and they show that species persistence occurs for a much larger set of parameter values when compared with inflexible consumers. Moreover, population dynamics will be chaotic when resource carrying capacities are high enough. This shows that adaptive consumer switching can destabilize population dynamics. r
Nonlinear Analysis: Theory, Methods & Applications, 2001
be a bounded domain in R n with a lipschitzian boundary @ , let D U , be open (in @ ) disjoint su... more be a bounded domain in R n with a lipschitzian boundary @ , let D U , be open (in @ ) disjoint subsets of @ , meas(@ \( D ∪ U )) = 0; meas D ¿ 0: (0.1) Let f; g : R 2 → R be di erentiable functions such that f(0; 0)=g(0; 0)=0. (Generally, we can suppose there are positive constants u, v such that f( u; v) = g( u; v) = 0 and require u = u, v = v on D in the boundary conditions (IC) and (CC) below. We can put u = v = 0, without loss of generality, and keep in mind that if u, v represent e.g. concentrations of two species in examples from biology then u, v should be positive.) Let us consider a reaction-di usion system u t = d 1 u + f(u; v); v t = d 2 v + g(u; v) on [0; +∞) × ;
Les origines des Slaves d'après les préhistoriens tchèques
Revue des études slaves, 1948
Nonlinear Analysis: Theory, Methods & Applications, 2006
A bifurcation problem for an elliptic multivalued boundary value problem with a real parameter is... more A bifurcation problem for an elliptic multivalued boundary value problem with a real parameter is considered. The existence of global bifurcation between two eigenvalues of a certain type of the Laplacian is proved. For a class of abstract inclusions with compact multivalued mappings in a Hilbert space, it is shown how the degree can be determined near the eigenvalues of a particular type of an associated linear single-valued problem, and the jump of the degree is proved. As a consequence, global bifurcation for such abstract inclusions is obtained. The weak formulation of the boundary value problem mentioned is a particular case. ᭧
Nonlinear Analysis: Theory, Methods & Applications, 2007
This paper concerns Crandall-Rabinowitz type bifurcation for abstract variational inequalities on... more This paper concerns Crandall-Rabinowitz type bifurcation for abstract variational inequalities on nonconvex sets and with multidimensional bifurcation parameter. We derive formulae which determine the bifurcation direction and, in the case of potential operators, the stability of all solutions close to the bifurcation point. In particular, it follows that in some cases an exchange of stability appears similar to the case of equations, but in some other cases stable nontrivial solutions bifurcate at points where there is no loss of stability of the trivial solution. As an application we consider a system of two second order ODEs with nonconvex unilateral boundary conditions.
Nonlinear Analysis: Theory, Methods & Applications, 2005
Variational inequalities on closed convex sets of a certain type (not cones in general) with a mu... more Variational inequalities on closed convex sets of a certain type (not cones in general) with a multidimensional parameter are considered, and local C k -smooth dependence of their solutions on the parameter is proved. The basic idea is to show that under some assumptions, the variational inequality is in a neighbourhood of a given solution equivalent to an equation for which implicit function theorem can be used. The result is applied to a model of a beam unilaterally supported by a finite number of fixed obstacles at different heights, and to Nash equilibria with parameters.
Nonlinear Analysis: Theory, Methods & Applications, 2010
Smooth dependence on data Signorini problem Variational inequality a b s t r a c t
Smooth bifurcation branches of solutions for a Signorini problem
Nonlinear Analysis: Theory, Methods & Applications, 2011
ABSTRACT We study a bifurcation problem for the equation Δu+λu+g(λ,u)u=0 on a rectangle with Sign... more ABSTRACT We study a bifurcation problem for the equation Δu+λu+g(λ,u)u=0 on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. Here λ∈R is the bifurcation parameter, and g is a small perturbation. We prove, under certain assumptions concerning an eigenfunction u0 corresponding to an eigenvalue λ0 of the linearized equation with the same nonlinear boundary conditions, the existence of a local smooth branch of nontrivial solutions bifurcating from the trivial solutions at λ0 in the direction of u0. The contact sets of these nontrivial solutions are intervals which change smoothly along the branch. The main tool of the proof is a local equivalence of the unilateral BVP to a system consisting of a corresponding classical BVP and of two scalar equations. To this system classical Crandall–Rabinowitz type local bifurcation techniques (scaling and Implicit Function Theorem) are applied.

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