Theory and Modern Applications
Page 93 of 98
The synchronization problem of new discrete-time complex networks with randomly occurring coupling and distributed time-varying delay is investigated. Compared with the previous work, the distributed delay is ...
This paper studies the problem of stabilization with optimal performance for dissipative DIHS (discrete-time impulsive hybrid systems). By using Lyapunov function method, conditions are derived under which the...
The second part of Hilbert's sixteenth problem concerned with the existence and number of the limit cycles for planer polynomial differential equations of degree n. In this article after a brief review on previou...
This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear, half-linear, super-half-linear, and nonlinear equations. Several oscillation crite...
We investigate the singular differential equation
on the half-line [
A linear second-order discrete-delayed equation
with a positive coefficient
It is found that every solution of a system of linear delay difference equations has finite limit at infinity, if some conditions are satisfied. These are much weaker than the known sufficient conditions for a...
This work presents sufficient conditions for the existence and uniqueness of positive solutions for a discrete fourth-order beam equation under Lidstone boundary conditions with a parameter; the iterative sequ...
-Euler Numbers and Polynomials
In 2009, Kim et al. gave some identities of symmetry for the twisted Euler polynomials of higher-order, recently. In this paper, we extend our result to the higher-order twisted ...
-Euler Numbers and Polynomials
We give a new construction of the
-extensions of Euler numbers and polynomials. We present new generating functions which are related to...
New oscillation criteria are established for second-order mixed-nonlinear delay dynamic equations on time scales by utilizing an interval averaging technique. No restriction is imposed on the coefficient funct...
The paper discusses the existence of positive solutions, dead-core solutions, and pseudo-dead-core solutions of the singular problem
,
-Laplacian-Like Operators
We investigate the following nonlinear equations with
-Laplacian-like operators
By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations
The existence and uniqueness of solutions and asymptotic estimate of solution formulas are studied for the following initial value problem:
The paper provides conditions sufficient for the existence of strictly increasing solutions of the second-order nonautonomous difference equation
We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the init...
By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations
This paper is concerned with a class of nonlinear delay partial difference equations with positive and negative coefficients, which also contains forcing terms. By making use of frequency measures, some new os...
Let
be a monic orthogonal polynomial sequence on the unit circle. We define recursively a new sequence
...
We investigate the effect of constant and periodic harvesting on the Beverton-Holt model in a periodically fluctuating environment. We show that in a periodically fluctuating environment, periodic harvesting g...
Many dynamical systems have an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process. The mathematical description of these phenomena leads to impulsive differenti...
A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equation
Yu. V. Nesterenko has proved that
,
,
...
We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations
on a time scale
...
The existence of asymptotically almost periodic mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay is studied.
The aim of this paper is to obtain new necessary and sufficient conditions for the uniform exponential stability of variational difference equations with applications to robustness problems. We prove character...
-Laplacian Equations
By topological degree theory and some analysis skills, we consider a class of generalized Liénard type
-Laplacian equations. Upon some suitable ...
A nonautonomous SIR epidemic model with age structure is studied. Using integro-differential equation and a fixed point theorem, we prove the existence and uniqueness of a positive solution to this model. We c...
We consider the propagator of an evolution equation, which is a semigroup of linear operators. Questions related to its operator norm function and its behavior at the critical point for norm continuity or compact...
-Genocchi Polynomials and Numbers of Higher Order
We investigate several arithmetic properties of
-Genocchi polynomials and numbers of higher order.
A new existence and uniqueness theorem is given for solutions to differential equations involving the Caputo fractional derivative with nonlocal initial condition in Banach spaces. An application is also given.
Systems are considered related to the control of processes described by oscillating second-order systems of differential equations with a single delay. An explicit representation of solutions with the aid of s...
We study several types of periodicity to a class of fractional order differential equations.
Some new oscillation criteria for the second-order neutral delay differential equation
,
...
Considering the linear delay difference system
, where
,
The permanence and the existence of periodic solution for a discrete nonautonomous competitive system with multidelays are considered. Also the stability of the periodic solution is discussed. Numerical exampl...
Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an a...
We consider a three-term nonlinear recurrence relation involving a nonlinear filtering function with a positive threshold
. We work out ...
We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations
on a time scale
...
In this paper, we consider the additive-cubic-quartic functional equation
and prove the generalized Hyers-Ulam stability of the additive-cubic-...
-Laplacian onTime Scales
The nonlocal boundary value problem, with
-Laplacian of the form
Positive Periodic Solutions to
-Species Nonautonomous Food Chains with Harvesting Terms
By using Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least
Let
be an integer with
, and let
...
We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay:
,
We provide a complete diagram of the relation between the admissibility of pairs of Banach function spaces and the exponential dichotomy of evolution families on the real line. We prove that if
This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions
We investigate global dynamics of the following systems of difference equations
,
Delay discrete inequalities with more than one nonlinear term are discussed, which generalize some known results and can be used in the analysis of various problems in the theory of certain classes of discrete...
A chemostat model with delayed response in growth and impulsive diffusion and input on nutrients is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism...
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