Theory and Modern Applications
Page 89 of 98
Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed type.
In this article, we investigate the boundedness property of the solutions of linear and nonlinear discrete Volterra equations in both convolution and non-convolution case. Strong interest in these kind of disc...
This article is devoted to studying uniqueness of difference polynomials sharing values. The results improve those given by Liu and Yang and Heittokangas et al.
The q-analogues of many well known formulas are derived by using several results of q-Bernoulli, q-Euler numbers and polynomials. The q-analogues of ζ-type functions are given by using generating functions of q-B...
In this article, we investigate existence of solutions for perturbed abstract measure functional differential equations. Based on the Arzelà-Ascoli theorem and the fixed point theorem, we give sufficient conditio...
In this article, we discuss the existence of periodic solutions for the higher-order difference equation
We consider the existence of single and multiple positive solutions for fourth-order Sturm-Liouville boundary value problem in Banach space. The sufficient condition for the existence of single and multiple po...
In this article, we discuss how to use a standard minimizing argument in critical point theory to study the existence of non-trivial homoclinic solutions of the following second-order non-autonomous discrete s...
In this article, we establish some stability criteria for the polar linear Hamiltonian dynamic system on time scales
Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equation
In this article, we study nonexistence, radial symmetry, and monotonicity of the positive solutions for a class of integral systems with weights. We use a new type of moving plane method introduced by Chen-Li-...
In this article, the results of theoretical research of the generalized hypercube function by generalizing two known functions referring to the cube hypervolume and hypersurface and the recurrent relation betw...
This paper develops and exposes the strong relationships that exist between time-domain order-distributions and the Laplace-domain logarithmic operator. The paper presents the fundamental theory of the Laplace...
A new approach for investigating polynomial solutions of differential equations is proposed. It is based on elementary linear algebra. Any differential operator of the form ...
Some new existence theorems for homoclinic solutions are obtained for a class of second-order discrete p-Laplacian systems by critical point theory, a homoclinic orbit is obtained as a limit of 2kT-periodic solut...
Based on a fixed point theorem in a cone, a new sufficient condition for the existence of a positive periodic solution to a class of higher-order functional difference equations is established in this article....
This article introduces a generalization for the Srivastava-Owa fractional operators in the unit disk. Conditions are given for the fractional integral operator to be bounded in Bergman space. Some properties ...
In this paper, we have investigated that initial time difference boundedness criteria and Lagrange stability for fractional order differential equation in Caputo's sense are unified with Lyapunov-like function...
Galilean invariance for general conservative finite difference schemes is presented in this article. Two theorems have been obtained for first- and second-order conservative schemes, which demonstrate the nece...
A diffusive model of pioneer and climax species interaction is considered. We perform a detailed Hopf bifurcation analysis to the model, and derive conditions for determining the bifurcation direction and the ...
In this article, we study a boundary value problem of a class of generalized linear discrete-time systems whose coefficients are square constant matrices. By using matrix pencil theory, we obtain formulas for ...
We reformulate the following additive functional equation with n-independent variables
Mustafa and Sims [Fixed Point Theory Appl. 2009, Article ID 917175, 10, (2009)] generalized a concept of a metric space and proved fixed point theorems for mappings satisfying different contractive conditions. In...
The linear neutral differential equation with variable delays is considered in this article. New criteria for asymptotic stability of the zero solution are established using the fixed point method and the diff...
In this paper, we establish sufficient conditions for the existence of a unique solution for a class of nonlinear non-autonomous system of Riemann-Liouville fractional differential systems with different const...
In this paper, we consider the rule of trajectory structure for a kind of second-order rational difference equation. With the change of the initial values, we find the successive lengths of positive and negati...
In this note, we establish some oscillation criteria for certain higher-order quasi-linear neutral differential equation. These criteria improve those results in the literature. Some examples are given to illu...
A 2m-point boundary value problem for a coupled system of nonlinear fractional differential equations is considered in this article. An existence result is obtained with the use of the coincidence degree theory.
In this article, we consider the following systems of Fredholm integral equations:
In this paper, by making use of the coincidence degree theory of Mawhin, the existence of the nontrivial solution for the boundary value problem with Riemann-Stieltjes Δ-integral conditions on time scales at r...
The main objective of this paper is to establish some new retarded nonlinear sum-difference inequalities with two independent variables, which provide explicit bounds on unknown functions. These inequalities g...
We study a superlinear Schrö dinger equation in the whole Euclidean space ℝ n . By using a suitable sign-changing critical point, we prove that the problem admits infinitely many...
This article studies the boundary value problems for the third-order nonlinear singular difference equations
In this paper, we prove the Hyers-Ulam stability of a functional equation related to inner product spaces in non-Archimedean normed spaces.
This paper is concerned about the dynamic behavior for the following high order nonlinear difference equation x n = (x n-k + x n-m + x n-l )...
This article addresses the problem of robust pseudo state feedback stabilisation of commensurate fractional order polytopic systems (FOS). In the proposed approach, Linear Matrix Inequalities (LMI) formalism i...
This paper performs a further investigation on the q-Bernoulli polynomials and numbers given by Açikgöz et al. (Adv. Differ. Equ. 2010, 9, Article ID 951764) some incorrect properties are revised. It is pointed o...
This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised. It i...
In this article, we prove the existence and uniqueness of solutions for a family of discrete boundary value problems for data f which belongs to a discrete Hilbert space W.
In this paper, we prove the generalized Hyers-Ulam stability of the following additive-cubic-quartic functional equation
In this paper, we present some new discrete Volterra-Fredholm type inequalities, based on which we study the qualitative and quantitative properties of solutions of a class of Volterra-Fredholm type difference...
We investigate global dynamics of the following systems of difference equations
In this article we study the difference equation
In this article, we deal with the existence, uniqueness, and a variation of solutions of the nonlinear control system with nonlinear monotone hemicontinuous and coercive operator. Moreover, the approximate con...
In this article, some Gronwall-type integral inequalities with impulses on time scales are investigated. Our results extend some known dynamic inequalities on time scales, unify and extend some continuous ineq...
In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generat...
By applying the fixed point theorem in cones, some new and general results on the existence of positive solution to second order generalized Sturm-Liouville dynamical system on time scale ...
In this paper, we consider the stability of generalized Cauchy functional equations such as
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