共查询到20条相似文献,搜索用时 534 毫秒
1.
The general ideal in this paper is to study a differential calculus for multivariable functions, directional ∇-derivative and curves of parametric equations on n-dimensional time scales.
相似文献
2.
Churong Chen Baoguo Jia Lynn Erbe Allan Peterson 《Journal of Difference Equations and Applications》2019,25(6):855-868
ABSTRACTWe study the nabla fractional difference system with retarded argument. There are two major ingredients. A Gronwall's inequality for the nabla case is given. This allows us to evaluate the solution of nabla fractional difference system. We shall illustrate the validity of our results by means of examples. 相似文献
3.
Zareen A. Khan 《Integral Transforms and Special Functions》2020,31(5):412-423
ABSTRACTThis paper investigates some system of integral inequalities of one independent variable on time scales. The conclusion can be obtained by using Hadamard-type fractional differential equations and Greene's method which bring together and expand some integral inequalities on time scales. The established inequalities give explicit bounds on unknown functions which can be utilized as a key in examining the properties of certain classes of partial dynamic equations and difference equations on time scales. As an application, a system of fractional differential equations is considered to explain the value of our results. 相似文献
4.
We give conditions on the coefficient matrix for certain perturbed linear dynamic equations on time scales ensuring that there exists a bounded solution (which is explicitly given) to which all other solutions converge, and similarly conditions ensuring a bounded solution from which all other solutions diverge. We also consider periodic time scales and corresponding linear dynamic equations with periodic coefficients and prove similar statements about periodic solutions to which all other solutions converge or from which all other solutions diverge. 相似文献
5.
Stefan Hilger 《Journal of Difference Equations and Applications》2013,19(10):897-936
We present "one-dimensional" Fourier theory on commutative groups T hH , 0 h h < X , 0< H h X within the framework of the so-called calculus on measure chains (or time scales). Depending on certain values of the graininess h and length H of the group the four classical types of Fourier transform are covered: Fourier integral ( T 0 X = R ), Fourier series ( T 1 X = Z ), Fourier analysis of periodic functions ( T 0,2 ~ = S 1 (0) unit circle) and discrete Fourier transform ( T 1 N = Z N ). We will present Fourier theory on these groups in a unified manner. This also allows to closely track the roles of the graininess h and length H of the group--especially for h M 0 and H M X . In the final part of the paper, we investigate the solution of a fundamental equation on T hH , which can be considered as a generalization of the Gauss function. It finally leads to a version of the Heisenberg uncertainty principle, which extends the classical one, valid for T 0 X = R , to the case T hH , where either h >0 or H < X . 相似文献
6.
Zhenjie Liu 《分析论及其应用》2009,25(4):369-380
This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis
functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence
degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time
scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method
is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference
equations. 相似文献
7.
Work with partial differential equations on time scales is just beginning. In this paper we explore a basic partial differential equation, search for solutions, and find conditions which generate solutions of a given type. 相似文献
8.
Here we solve two problems presented in paper [9] (C C Tisdell and A Zaidi, Basic qualitative and quantitative results for
solutions to nonlinear, dynamic equations on time scales with an application to economic modelling, Nonlinear Anal.
68 (2008) 3504–3524). We study existence and uniqueness of solutions for delay systems and first-order dynamic equations of
the form x
Δ = f (t,x,x
σ
) on time scales by using the Banach’s fixed-point theorem. Some examples are presented to illustrate the efficiency of the
proposed results. 相似文献
9.
Meiqiang Feng Hanying Feng Xuemei Zhang Weigao Ge 《Mathematical and Computer Modelling》2008,48(7-8):1213-1226
This paper deals with a class of second-order nonlinear m-point dynamic equation on time scales with one-dimensional p-Laplacian. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order delta derivative explicitly. Meanwhile, an example is worked out to demonstrate the main results. 相似文献
10.
The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds
on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities
related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl.
251 (2000) 736–751). 相似文献
11.
12.
《Quaestiones Mathematicae》2013,36(3):349-379
Abstract The properties of the limit cycle of a generalised van der Pol equation of the form ü + u = ε (1—u2n)u, where ε is small and n is any positive integer, are investigated by applying a time transformation perturbation method due to Burton. It is found that as n increases the amplitude of the limit cycle oscillation decreases and its period increases. The time transformation solution is compared with the solution derived using the method of multiple scales and with a numerical solution. It is found that, to first order in ε, the time transformation solution for the limit cycle agrees better with the numerical solution than the multiple scales solution. Both perturbation solutions give the same result for the period of the limit cycle to second order in ε. The accuracy of the time transformation solution decreases as n increases. 相似文献
13.
14.
《复变函数与椭圆型方程》2012,57(10):867-880
We study the continuous, desingularized Newton method for Weierstrass' ?-functions. This leads to a family of autonomous differential equations in the plane, which depends on two complex parameters ω 1 and ω 2. For the associated flows there are, up to conjugacy, precisely three possibilities. These are determined by the form of the parallelogram spanned by ω 1 and ω 2: square, rectangular but not square, and non-rectangular. 相似文献
15.
16.
《复变函数与椭圆型方程》2012,57(2):167-176
We prove in this paper that, given a nonempty open set G in the complex plane, a subset A of G which is not relatively compact and a holomorphic infinite order differential or antidiffeärential operator T, then there are holomorphic functions ? on G such that the image of A under T ? is dense in the complex plane. This extends a recent result about a property of boundary behaviour exhibited by the derivative operator. 相似文献
17.
Gerald Rosen 《Journal of Difference Equations and Applications》2013,19(1):25-32
It is shown here that a 3 2 4 lattice in the wall for TeV quantum gravity with n =2 extra small-scale spatial dimensions can account for the fermion masses in a strikingly accurate manner. The family index, the electromagnetic charge number coupling, and the Yukawa coupling for lepton and quark mass generation in the minimal Standard Model (with a single Higgs) are related here to t' Hooft discreteness in the wall. Discrete values for the two transverse spatial distances in the wall are viewed as geometrical correspondents of the family index and the electromagnetic charge number coupling. The mass spectrum of Dirac leptons and quarks can then be understood as a manifestation of a Yukawa coupling that depends on the transverse wall coordinates. Linear homogeneous difference equations are considered to govern the Yukawa coupling or, more appropriately, the Yukawa field on the wall lattice. The solution to the latter difference equations yields experimentally consistent pole mass values for all twelve leptons and quarks. With the Yukawa field extending through the bulk, mass elevation for the second and third families features the torus radii ratio R 2 / R 1 =41/10. 相似文献
18.
《复变函数与椭圆型方程》2012,57(8):731-743
Gibbs phenomenon occurs for most approximations based on standard orthogonal expansions, as well as for those based on integral operators. It also occurs in interpolations and other types of approximations. We consider a general approach to approximation based on delta sequences in an attempt to better understand the concept. 相似文献
19.
In this paper we introduce linear graininess (LG) time scales. We further study orthogonal polynomials (OPs) with the weight function supported on LG time scales and derive the raising and lowering ladder operators by using the time scales calculus. We also derive a second order dynamic equation satisfied by these polynomials. The notion of an LG time scale encompasses the cases of the reals, the h-equidistant grid, the q-grid and, more general, a mixed (q, h)-grid. This allows a unified treatment of the ladder operators theory for classical OPs on these time scales. Moreover we will explain, why exclusively LG time scales provide the right framework for general OP theory. 相似文献
20.
F. Merdivenci Atici Alberto Cabada Juan B. Ferreiro 《Journal of Difference Equations and Applications》2013,19(4):357-370
In this paper, we establish comparison results (maximum principles) which allow us to use the monotone method and the method of upper and lower solutions in order to build convergent sequences to the solutions of difference equations of the type j u k = f k , u k +1 , max l ] { k m h +1,…, k +1} u l , k ] I , u 0 = u T , with j u k = u k +1 m u k , I ={0,1,…, T m 1} and f ] C ( I 2 R 2 R , R ). 相似文献