Theory and Modern Applications
Page 87 of 98
We establish the Rofe-Beketov formula for symplectic systems on time scales. This result generalizes the well-known d’Alembert formula (or the Reduction of Order Theorem) and the Rofe-Beketov formula published...
We establish new comparison theorems, to offer criteria for all nonoscillatory solutions of the third-order functional differential equation
In this article, we establish the new result on homoclinic orbits for a class of damped vibration systems. Some recent results in the literature are generalized and significantly improved.
We consider the nonoscillatory half-linear difference equation
We study the scalar p-degree functional
In this article, a class of fourth-order difference equations with quasi-differences and deviating argument is considered. We state a new oscillation theorem for the sublinear case and we complete the existing...
In this article, we investigate the Hyers-Ulam stability of the following functional equation
In this article, we study the boundary value problems for the fourth-order nonlinear coupled difference equations
A predator-prey model with simplified Holling type III response function incorporating a prey refuge under sparse effect is considered. Through qualitative analysis of the model, at least two limit cycles exis...
Let ℙ n be the space of polynomials of degree less than or equal to n. In this article, using the Bernoulli basis {B0(x), . . . , B n (x)} for ...
This article studies a boundary value problem of nonlinear fractional differential equations with three-point fractional integral boundary conditions. Some new existence results are obtained by applying standa...
This paper deals with an application of the method of quasilinearization by not demanding the Hölder continuity assumption of functions involved and by choosing upper and lower solutions with initial time diff...
We show that for C1-generic f, a locally maximal homoclinic class is usual limit shadowable if and only if the homoclinic class is hyperbolic.
We study the existence of positive periodic solutions of the second-order difference equation
In this article, we consider a strongly coupled model of plankton allelopathy. Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions fo...
In this article, we consider the impulsive stabilization of delay difference equations. By employing the Lyapunov function and Razumikhin technique, we establish the criteria of exponential stability for impul...
In this article, we solve the open problem 24.5.6 given in the study of Ismail, which consists of extending the action of q-translation operators introduced by Ismail to some measurable functions by means of basi...
In this article, we introduce the q-variant of Beta operator. We find the recurrence formula for m th-order moments. Here, we establish some direct theorems in terms of modulus of continuity for these operators. ...
A mass conserved time-splitting difference method is presented for the one-dimensional dipolar Bose-Einstein condensates (BECs) described by a nonlocal nonlinear Schrödinger equation with a convolution term. A...
In this paper, a Holling II two-pery one-predator system is investigated. Based on the continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov function, we derive a set of suf...
In this article, we prove some fixed point theorems of Geraghty-type concerning the existence and uniqueness of fixed points under the setting of modular metric spaces. Also, we give an application of our main...
In this article we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter λ. This nonlinear dependence on λ is allowe...
This paper studies a nonlocal boundary value problem of nonlinear third-order q-difference equations. Our results are based on Leray-Schauder degree theory and some standard fixed point theorems.
In this article, we investigate the generalized Hyers-Ulam-Rassias stability, Isac-Rassias type stability and superstability of ternary homomorphisms and ternary derivations associated to the generalized m- varia...
This paper discusses the existence of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions in Hilbert spaces. The discussion is based on analytic semigroups theory an...
The algorithm of singular point quantities for an equilibrium of three-dimensional dynamics system is studied. The explicit algebraic equivalent relation between singular point quantities and Liapunov constant...
In this paper, we first introduce a concept of the mean-value of uniformly almost periodic functions on time scales and give some of its basic properties. Then, we propose a concept of pseudo almost periodic f...
In this work, the existence criteria of extremal solutions of periodic boundary value problems for the first-order dynamic equations on time scales are given by using the method of lower and upper solutions co...
In this article, we study the stability of a class of singular linear matrix difference equations whose coefficients are square constant matrices and the leading coefficient matrix is singular. Speciffically w...
This article studies the existence and dimension of the set for mild solutions of semilinear fractional differential inclusions. We recall and prove some new results on multivalued maps to establish our main r...
This article considers both the static output feedback stabilization issue and output-feedback guaranteed cost controller design of a class of discrete-time nonlinear systems with time-delay. First, by static ...
In this article, we consider the existence of positive solutions of the (n - 1, 1) conjugate-type nonlocal fractional differential equation
In this article, we establish the generalized Hyers-Ulam (or Hyers-Ulam-Rassais) stability of Jordan homomorphisms and Jordan derivations of the following parametric additive functional equation:
In this article we study the global convergence result, boundedness, and periodicity of solutions of the difference equation
In this article, using comparison with second-order dynamic equations, we establish sufficient conditions for oscillatory solutions of an n th-order neutral dynamic equation with distributed deviating arguments. ...
Some new criteria for the oscillation of n th order nonlinear dynamic equations of the form
In this article, by using the fixed point theorem, existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations
In this article, we prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical A-summability. We also study the rate of statistical A-summability of positive li...
The existence and uniqueness of the Korteweg-de Vries type equation with time delay are investigated. The problem is formulated as an abstract quasi-linear function differential equation. The solution is studi...
In this article, we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in paranormed spaces.
Our aim in this work is to study the existence and the attractivity of solutions for a system of delay partial integro-differential equations of fractional order. We use the Schauder fixed point theorem for th...
In this article, by using Razumikhin-type technique, we investigate p th moment exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses. Several stabili...
Integral transform methods are widely used to solve the several dynamic equations with initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform...
We use the derivative sampling theorem (Hermite interpolations) to compute eigenvalues of a discontinuous regular Dirac systems with transmission conditions at the point of discontinuity numerically. We closel...
In this article, we revise results obtained by Han et al.
This article studies the necessary and sufficient conditions for asymptotic stability of the linear positive systems with bounded time-varying delays on time scales. Using Lyapunov functions, asymptotic stabil...
In this paper we consider the differential difference operator
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