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Competitive Exclusion in a Discrete Stage-Structured Two Species Model

A. S. Ackleh, P. Zhang (2009)

Mathematical Modelling of Natural Phenomena

We develop a stage-structured model that describes the dynamics of two competing species each of which have sexual and clonal reproduction. This is typical of many plants including irises. We first analyze the dynamical behavior of a single species model. We show that when the inherent net reproductive number is smaller than one then the population will go to extinction and if it is larger than one then an interior equilibrium exists and it is globally asymptotically stable. Then we analyze...

Conjugacy criteria for second order linear difference equations

Ondřej Došlý, Pavel Řehák (1998)

Archivum Mathematicum

We establish conditions which guarantee that the second order difference equation Δ 2 x k + p k x k + 1 = 0 possesses a nontrivial solution with at least two generalized zero points in a given discrete interval

Conjugation to a shift and the splitting of invariant manifolds

Vassiliĭ Gelfreich (1997)

Applicationes Mathematicae

We give sufficient conditions for a diffeomorphism in the plane to be analytically conjugate to a shift in a complex neighborhood of a segment of an invariant curve. For a family of functions close to the identity uniform estimates are established. As a consequence an exponential upper estimate for splitting of separatrices is established for diffeomorphisms of the plane close to the identity. The constant in the exponent is related to the width of the analyticity domain of the limit flow separatrix....

Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs

Rafael Company, Lucas Jódar, José-Ramón Pintos (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the numerical solution of nonlinear Black-Scholes equation modeling European vanilla call option pricing under transaction costs. Using an explicit finite difference scheme consistent with the partial differential equation valuation problem, a sufficient condition for the stability of the solution is given in terms of the stepsize discretization variables and the parameter measuring the transaction costs. This stability condition is linked to some properties of the numerical...

Continuous dependence on parameters for second order discrete BVP’s

Marek Galewski, Szymon Głąb (2012)

Open Mathematics

Using Fan’s Min-Max Theorem we investigate existence of solutions and their dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the relevant Euler action functional.

Convexity and almost convexity in groups

Witold Jarczyk (2013)

Banach Center Publications

We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance...

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