共查询到20条相似文献,搜索用时 31 毫秒
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Takafumi Miyazaki 《The Ramanujan Journal》2018,45(3):601-613
For any given odd prime p and a fixed positive integer D prime to p, we study the equation \(x^2+D^m=p^n\) in positive integers x, m and n. We use a classical work of Dem’janenko in 1965 on a certain quadratic Diophantine equation together with some results concerning the existence of primitive divisors of Lucas sequences to examine our equation when D is a product of \(p-1\) and a square. 相似文献
3.
Thomas Riedel 《Aequationes Mathematicae》1991,41(1):192-211
Summary Recently R. C. Powers characterized the order automorphisms of the space of nondecreasing functions from one compact real interval to another [6, 7]. In this paper we show how his results, as well as the lattice-theoretic techniques which he employed, can be used to obtain solutions of Cauchy's equation for certain classes of semigroups (triangle functions) on the space + of probability distribution functions of nonnegative random variables. 相似文献
4.
《Chaos, solitons, and fractals》2000,11(5):791-798
By using the definition of the characteristic function and Kramers–Moyal Forward expansion, one can obtain the Fractional Fokker–Planck Equation (FFPE) in the domain of fractal time evolution with a critical exponent α (0<α⩽1). Two different classes of fractional differential operators, Liouville–Riemann (L–R) and Nishimoto (N) are used to represent the fractal differential operators in time. By applying the technique of eigenfunction expansion to get the solution of FFPE, one finds that the time part of eigenfunction expansion in terms of L–R represents the waiting time density Ψ(t), which gives the relation between fractal time evolution and the theory of continuous time random walk (CTRW). From the principle of maximum entropy, the structure of the distribution function can be known. 相似文献
5.
ZHANG Rui-feng~ GUO Bo-ling~ Institute of Appl.Math. College of Math.and Inform.Sci. Henan Univ. Kaifeng China Institute of Appl.Phys.and Comput.Math. Beijing China. 《高校应用数学学报(英文版)》2008,23(1):57-64
The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k. 相似文献
6.
Mikio Murata 《Journal of Difference Equations and Applications》2013,19(6):1008-1021
A systematic approach to the construction of ultradiscrete analogues for differential systems is presented. This method is tailored to first-order differential equations and reaction–diffusion systems. The discretizing method is applied to Fisher–KPP equation and Allen–Cahn equation. Stationary solutions, travelling wave solutions and entire solutions of the resulting ultradiscrete systems are constructed. 相似文献
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We solve generalized the generalized Rubel equation on the space of analytic functions in domains. 相似文献
9.
The Cushing–Henson conjectures on time scales are presented and verified. The central part of these conjectures asserts that based on a model using the dynamic Beverton–Holt equation, a periodic environment is deleterious for the population. The proof technique is as follows. First, the Beverton–Holt equation is identified as a logistic dynamic equation. The usual substitution transforms this equation into a linear equation. Then the proof is completed using a recently established dynamic version of the generalized Jensen inequality. 相似文献
10.
An equation involving a derivative is called a differential equation.Such as,dy/dx=2x,and the function y=f(x)satisfies this equation.When we know the additional condition that y=2 when x=-1,the function y=f(x)will be find exactly.The additional condition is called the initial condition.It is used to evaluate constant of integration. 相似文献
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Gunnar Aronsson 《manuscripta mathematica》1986,56(2):135-158
Here, all solutions of the form u=rkf() to the p-harmonic equation, div(|u|p–2u)=0, (p>2) in the plane are determined. One main result is a representation formula for such solutions. Further, solutions with an isolated singularity at the origin are constructed (Theorem 1). Graphical illustrations are given at the end of the paper. Finally, all solutions u=rkf() of the limit equation for p=, u
x
2
uxx+2uxuyuxy+u
y
2
uyy=2, are constructed, some of which have a strong singularity at the origin (Theorem 2). 相似文献
13.
《Applied Mathematics Letters》2001,14(6):759-763
We deal with the inclusion of exchange effects in the self-consistent one particle Schrödinger equation. For the stationary case local approximations (of the Hartree-Fock equations) can be rigorously justified. By heuristically using these terms in the time dependent case we add the local exchange potential of the Xα method to the Hartree equations. Thus, we obtain the “Schrödinger-Poisson-Xα” model where the effective potential is the difference of the nonlocal Coulomb potential and the third root of the local density. 相似文献
14.
Kamel Al-Khaled 《Applications of Mathematics》2014,59(4):441-452
This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers’ equation. The approximate solution is shown to converge to the exact solution at an exponential rate. A numerical example is given to illustrate the accuracy of the method. 相似文献
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《Chaos, solitons, and fractals》2003,15(1):131-139
It is shown that motion of plane curves in affine geometry induces naturally the Sawada–Kotera hierarchy. The affine Sawada–Kotera equation is obtained in view of the equivalence of equations for the curvature and graph of plane curves when the curvature satisfies the Sawada–Kotera equation. The affine Sawada–Kotera equation can be viewed as an affine version of the WKI equation since they have similarity properties, such as they have loop-solitons, they are solved by the AKNS-scheme and are obtained by choosing the normal velocity to be the derivative of the curvature with respect to the arc-length. Its symmetry reductions to ordinary differential equations corresponding to an one-dimensional optimal system of its Lie symmetry algebras are discussed. 相似文献
16.
Flank D.M. Bezerra Alexandre N. Carvalho Tomasz Dlotko Marcelo J.D. Nascimento 《Journal of Mathematical Analysis and Applications》2018,457(1):336-360
We consider the Dirichlet boundary problem for semilinear fractional Schrödinger equation with subcritical nonlinear term. Local and global in time solvability and regularity properties of solutions are discussed. But our main task is to describe the connections of the fractional equation with the classical nonlinear Schrödinger equation, including convergence of the linear semigroups and continuity of the nonlinear semigroups when the fractional exponent α approaches 1. 相似文献
17.
Jean-Luc Marichal 《Aequationes Mathematicae》2010,79(3):237-260
We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x) = F(G(x), . . . , G(x)), where F is a given function of n real variables. We provide necessary and sufficient conditions on F for the existence and uniqueness of solutions. When F is nondecreasing in each variable, we show in a constructive way that if a solution exists then a nondecreasing and idempotent
solution always exists. We also provide necessary and sufficient conditions on F for the existence of continuous solutions and we show how to construct such a solution. We finally discuss a few applications
of these results. 相似文献
18.
In this paper the Cauchy problem for the following nonhomogeneous Burgers’ equation is considered : (1)u
t
+uu
x
=μu
xx
−kx,x ∈R,t > 0, where μ and k are positive constants. Since the nonhomogeneous term kx does not belong to any Lp(R) space, this type of equation is beyond usual Sobolev framework in some sense. By Hopf-Cole transformation, (1) takes the
form (2)ϕ
t
−ϕ
xx
= −x
2
ϕ. With the help of the Hermite polynomials and their properties, (1) and (2) are solved exactly. Moreover, the large time
behavior of the solutions is also considered, similar to the discussion in Hopf’s paper. Especially, we observe that the nonhomogeneous
Burgers’ equation (1) is nonlinearly unstable. 相似文献
19.
《中学生数学》2014,(13)
<正>An equation involving a derivative is called a differential equation.Such as,(dy)/(dx)=2x,and the function y=f(x)satisfies this equation.When we know the additional condition that y=2when x=-1,the function y=f(x)will be find exactly.The additional condition is called the initial condition.It is used to evaluate constant of integration. 相似文献