Theory and Modern Applications
Page 95 of 98
We study discrete almost automorphic functions (sequences) defined on the set of integers with values in a Banach space
. Given a bounded linear...
This paper studies Sturm-Picone comparison theorem of second-order linear equations on time scales. We first establish Picone identity on time scales and obtain our main result by using it. Also, our result un...
The existence of periodic, almost periodic, and asymptotically almost periodic of periodic and almost periodic of abstract retarded functional difference equations in phase spaces is obtained by using stabilit...
-Laplacian Dynamic Equations on Time Scales
We analytically establish the conditions for the existence of at least two or three positive solutions in the generalized
-point boundar...
This paper is devoted to derive some sufficient conditions for the existence and uniqueness of positive solutions to a singular second-order dynamic equation with Dirichlet boundary conditions.
-Laplacian on Time Scales
We consider the existence of positive solutions for a class of second-order multi-point boundary value problem with
-Laplacian on time scales. B...
This paper studies general coupled boundary value problems for second-order difference equations. Existence of eigenvalues is proved, numbers of their eigenvalues are calculated, and their relationships betwee...
We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form
The spectrum containment of almost periodic solution of second-order neutral delay differential equations with piecewise constant of argument (EPCA, for short) of the form
We obtain new explicit exponential stability results for difference equations with several variable delays and variable coefficients. Several known results, such as Clark's asymptotic stability criterion, are ...
Planar linear discrete systems with constant coefficients and weak delay are considered. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In...
-Laplacian BVP with Sign-Changing Nonlinearity Involving Derivative on Time Scales
Let
be a time scale such that
. By using a monotone iterati...
This paper studies the global asymptotic stability for positive solutions to the higher order rational difference equation
, where
This paper considers a new class of additive neural networks where the neuron activations are modelled by discontinuous functions with nonlinear growth. By Leray-Schauder alternative theorem in differential in...
Criteria are established for existence of least one or three positive solutions for boundary value problems of second-order functional dynamic equations on time scales. By this purpose, we use a fixed-point in...
We establish sufficient conditions for the existence of mild solutions for some densely defined semilinear functional differential equations and inclusions involving the Riemann-Liouville fractional derivative...
The impulsive control method is developed to stabilize a class of neural networks with both time-varying and distributed delays. Some exponential stability criteria are obtained by using Lyapunov functionals, ...
We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of
Switching controller design for a class of Markovian jump nonlinear systems with unmodeled dynamics is considered in this paper. Based on the differential equation and infinitesimal generator of jump systems, ...
We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of ...
We consider the general solution of quartic functional equations and prove the Hyers-Ulam-Rassias stability. Moreover, using the pullbacks and the heat kernels we reformulate and prove the stability results of...
We consider an
-dimensional version of the functional equations of Aczél and Chung in the spaces of generalized functions such as the Sc...
We investigate certain sum-difference inequalities in two variables which provide explicit bounds on unknown functions. Our result enables us to solve those discrete inequalities considered by Sheng and Li (20...
We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomir...
This paper investigates the existence of periodic solutions of a ratio-dependent predator-prey diffusion system with Michaelis-Menten functional responses and time delays in a two-patch environment on time sca...
This paper deals with singularly perturbed initial value problem for linear first-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives...
We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential an...
For positive linear Volterra difference equations in Banach lattices, the uniform asymptotic stability of the zero solution is studied in connection with the summability of the fundamental solution and the inv...
We first give a theorem on the reducibility of linear system of difference equations of the form
. Next, by the means of Floquet theory,...
We study the existence of almost periodic solutions for nonlinear discrete Volterra equations with unbounded delay, as a discrete analogue of the results for integro-differential equations by Y. Hamaya (1993).
We study the existence, multiplicity, and nonexistence of positive solutions for multiparameter semipositone discrete boundary value problems by using nonsmooth critical point theory and subsuper solutions met...
Linear Dynamic Systems on Time Scales
We establish WKB estimates for
linear dynamic systems with a small parameter
...
This paper is devoted to using perturbation and variational techniques to derive some sufficient conditions for the existence of multiple positive solutions in the sense of distributions to a singular second-o...
Consider the multiplicity of solutions to the nonlinear second-order discrete problems with minimum and maximum:
,
...
-Laplacian Functional Dynamic Equations on Time Scales
This paper is concerned with the existence and nonexistence of positive solutions of the
-Laplacian functional dynamic equation on a tim...
We investigate the existence of almost-periodic weak solutions of second-order neutral delay-differential equations with piecewise constant argument of the form
...
It is supposed that the fractional difference equation
,
ha...
The half-linear difference equations with the deviating argument
,
We show that every solution of the following system of difference equations
,
...
At the price of sacrificing all suspense, we can already announce that the answer to the question of the title is "no." It is indeed our belief that one may find counterexamples to all integrability conjectures,
This article analyses the asymptotic behaviour of solutions of linear Volterra difference equations. Some sufficient conditions are presented under which the solutions to a general linear equation converge to ...
Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineerin...
We examine the various types of stability for the solutions of linear dynamic systems on time scales and give two examples.
-Euler Numbers and Polynomials Associated with
-Adic
-Integrals
By using
-adic
-integrals on
...
We offer criteria for the existence of positive solutions for two-point right focal eigenvalue problems
,
...
The aim of this paper is to study the superstability related to the d'Alembert, the Wilson, the sine functional equations for the trigonometric functional equations as follows: ...
We study the difference equation
,
,
...
We investigate the global stability character of the equilibrium points and the period-two solutions of
...
We study a discrete delay Mosquito population equation. Firstly, we study the stability of the equilibria of the system and the existence of period-two bifurcation by analyzing the characteristic equation. Second...
Values of λ are determined for which there exist positive solutions of the system of dynamic equations,
,
...
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