Center conditions for a simple class of quintic systems.
Chaos in some planar nonautonomous polynomial differential equation
We show that under some assumptions on the function f the system generates chaotic dynamics for sufficiently small parameter ϕ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.
Chaotic dynamics and nonlinear feedback control
Chemotaxis models with a threshold cell density
We consider a quasilinear parabolic system which has the structure of Patlak-Keller-Segel model of chemotaxis and contains a class of models with degenerate diffusion. A cell population is described in terms of volume fraction or density. In the latter case, it is assumed that there is a threshold value which the density of cells cannot exceed. Existence and uniqueness of solutions to the corresponding initial-boundary value problem and existence of space inhomogeneous stationary solutions are discussed....
Cohomology and Morse theory for strongly indefinite functionals.
Comments on “A new method for the explicit integration of Lotka-Volterra equations”.
Constant invariant solutions of the Poincaré center-focus problem.
Construction of non-constant lower and upper functions for impulsive periodic problems.
Constructive method for solving a nonlinear singularly perturbed system of differential equations in critical case.
Continuous dependence on parameters and boundedness of solutions to a hysteresis system
We analyze an ordinary differential system with a hysteresis-relay nonlinearity in two cases when the system is autonomous or nonautonomous. Sufficient conditions for both the continuous dependence on the system parameters and the boundedness of the solutions to the system are obtained. We give a supporting example for the autonomous system.
Contractive mappings and periodically perturbed conservative systems
Contributions of Alan C. Lazer to mathematical population dynamics.
Convergence acceleration of shifted transformations for totally nonnegative Hessenberg matrices
We design shifted transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted transformations by considering the concept of the Newton shift....
Correction to our paper “Periodic solutions to abstract differential equations”
Corrections to "Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas" (Dissertationes Math. 291 (1990))
Critical Point Theorems for Indefinite Functionals.