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.
Singular second-order multipoint dynamic boundary value problems with mixed derivatives.
Sistemas lineales singulares de dos ecuaciones en diferencias finitas de primer orden de coeficientes constantes y de valores iniciales aleatorios. Aplicaciones.
Skolem–Mahler–Lech type theorems and Picard–Vessiot theory
We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem–Mahler–Lech theorem to rational function coefficients. The second problem is whether or not for a given linear difference equation there exists a Picard–Vessiot extension inside the ring of sequences. The third problem is a certain special case of the dynamical Mordell–Lang conjecture. This allows us to deduce...
Smooth and discrete systems -- algebraic, analytic, and geometrical representations.
Smoothness of solutions of conjugate boundary-value problems on a measure chain.