Some complements of Cauchy's inequality on time scales.
Some discrete Poincaré-type inequalities.
Some new discrete inequalities and their applications.
Some new discrete nonlinear delay inequalities and application to discrete delay equations.
Some nonlinear delay integral inequalities and their discrete analogues.
Some notes on oscillation of two-dimensional system of difference equations
Oscillatory properties of solutions to the system of first-order linear difference equations are studied. It can be regarded as a discrete analogy of the linear Hamiltonian system of differential equations. We establish some new conditions, which provide oscillation of the considered system. Obtained results extend and improve, in certain sense, results presented in Opluštil (2011).
Some open problems on the solutions of the delay difference equation .
Some Perturbation Results On Multivalued Difference Equations
Some properties of solutions of a class of nonlinear difference equations
Some properties of solutions of complex q-shift difference equations
Combining difference and q-difference equations, we study the properties of meromorphic solutions of q-shift difference equations from the point of view of value distribution. We obtain lower bounds for the Nevanlinna lower order for meromorphic solutions of such equations. Our results improve and extend previous theorems by Zheng and Chen and by Liu and Qi. Some examples are also given to illustrate our results.
Some remarks on the general theorem of the existence of iterative roots of homeomorphisms with a rational rotation number
We show that the theorem proved in [8] generalises the previous results concerning orientation-preserving iterative roots of homeomorphisms of the circle with a rational rotation number (see [2], [6], [10] and [7]).
Some results on stability of difference systems.
Some roughness results concerning reducibility for linear difference equations.
Spatial discretization of an impulsive Cohen-Grossberg neural network with time-varying and distributed delays and reaction-diffusion terms.
Special solutions of linear difference equations with infinite delay
For the difference equation ,where is a Banach space, is a parameter and is a linear, bounded operator. A sufficient condition for the existence of a unique special solution passing through the point is proved. This special solution converges to the solution of the equation (0) as .
Spectral analysis of unbounded Jacobi operators with oscillating entries
We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the OP family...
Spectral deformations of Jacobi operators.
Spectral properties of the monodromy matrix for Harper equation
Spectral theory from the second-order -difference operator.
Spectral theory of corrugated surfaces
We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.