Results and conjectures about order Lyness' difference equation in , with a particular study of the case .
Results on the deficiencies of some differential-difference polynomials of meromorphic functions
In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c). The main results of this paper are listed as follows: Let f(z) be a meromorphic function of finite order satisfying lim sup r→+∞ T(r, f) T(r, f ′ ) <+∞, and c be a non-zero complex constant, then δ(∞, f(z)m f(z+c)f′(z))≥δ(∞, f′) and δ(∞,f(z+c)nf′(z))≥ δ(∞, f′). We also investigate the value...
Resurgence relations for classes of differential and difference equations
Riccati matrix differential equation and the discrete order preserving property
In this paper we recall discrete order preserving property related to the discrete Riccati matrix equation. We present results obtained by applying this property to the solutions of the Riccati matrix differential equation.
Ruelle operator with nonexpansive IFS
The Ruelle operator and the associated Perron-Frobenius property have been extensively studied in dynamical systems. Recently the theory has been adapted to iterated function systems (IFS) , where the ’s are contractive self-maps on a compact subset and the ’s are positive Dini functions on X [FL]. In this paper we consider Ruelle operators defined by weakly contractive IFS and nonexpansive IFS. It is known that in such cases, positive bounded eigenfunctions may not exist in general. Our theorems...
Šarkovského věta a diferenciální rovnice
Šarkovského věta a diferenciální rovnice. II
Secant tree calculus
A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.
Second order difference inclusions of monotone type
The existence of anti-periodic solutions is studied for a second order difference inclusion associated with a maximal monotone operator in Hilbert spaces. It is the discrete analogue of a well-studied class of differential equations.
Second order linear difference equations over discrete Hardy fields
We shall investigate the properties of solutions of second order linear difference equations defined over a discrete Hardy field via canonical valuations.
Second order linear -difference equations: nonoscillation and asymptotics
The paper can be understood as a completion of the -Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear -difference equations. The -Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice with . In addition to recalling the existing concepts of -regular variation and -rapid variation we introduce -regularly bounded functions and prove many related properties. The -Karamata theory is then...
Second-order -point eigenvalue problems on time scales.
Self-adjoint boundary-value problems on time-scales.
Séries de -factorielles, opérateurs aux -différences et confluence
Sets of -recurrence but not -recurrence
For every , we produce a set of integers which is -recurrent but not -recurrent. This extends a result of Furstenberg who produced a -recurrent set which is not -recurrent. We discuss a similar result for convergence of multiple ergodic averages. We also point out a combinatorial consequence related to Szemerédi’s theorem.
Several existence theorems of nonlinear -point BVP for an increasing homeomorphism and homomorphism on time scales.
S-hermitian boundary-value problems for difference systems.
Sign-changing solutions for discrete second-order three-point boundary value problems.
Singular bilateral boundary value problems for discrete generalized Lyapunov matrix equations.
Existence and uniqueness conditions for solving singular initial and two-point boundary value problems for discrete generalized Lyapunov matrix equations and explicit expressions of solutions are given.
Singular boundary value problem on infinite time scale.