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1.
A. O. Savchenko 《Theoretical and Mathematical Physics》2014,179(2):574-587
We investigate properties of sets of functions comprising countably many elements An such that every function An is orthogonal to all polynomials of degrees less than n. We propose an effective method for solving Fredholm integral equations of the first kind whose kernels are generating functions for these sets of functions. We study integral equations used to solve some axially symmetric problems in physics. We prove that their kernels are generating functions that produce functions in the studied families and find these functions explicitly. This allows determining the elements of the matrices of systems of linear equations related to the integral equations for considering the physical problems. 相似文献
2.
On the reflecting function and the qualitative behavior of solutions of some non-autonomous differential equations
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Zhengxin Zhou 《Journal of Applied Analysis & Computation》2017,7(2):523-531
In this article, we use the Mironenko''s method to discuss the qualitative behavior of some non-autonomous differential equations. We study the structure of the reflecting functions of the simplest differential equations, and obtain some sufficient conditions under which these equations have the rational reflecting functions. We apply the obtained results to discuss the numbers of periodic solutions of the non-autonomous differential systems and derive some sufficient conditions for a critical point of theirs to be a center. 相似文献
3.
Analysis of the Bernstein basis functions: an approach to combinatorial sums involving binomial coefficients and Catalan numbers
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Yilmaz Simsek 《Mathematical Methods in the Applied Sciences》2015,38(14):3007-3021
We give some alternative forms of the generating functions for the Bernstein basis functions. Using these forms,we derive a collection of functional equations for the generating functions. By applying these equations, we prove some identities for the Bernstein basis functions. Integrating these identities, we derive a variety of identities and formulas, some old and some new, for combinatorial sums involving binomial coefficients, Pascal's rule, Vandermonde's type of convolution, the Bernoulli polynomials, and the Catalan numbers. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
4.
We show that many general results on Hyers–Ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem. The theorem is formulated for self-maps of some subsets of the space of functions from a nonempty set into the set of reals. We also give some applications of that theorem, e.g., in investigations of solutions of some difference equations and functional inequalities. 相似文献
5.
M. S. Syavavko 《Ukrainian Mathematical Journal》1996,48(8):1282-1298
We present a method for solution of linear ill-posed equations in function spaces based on the use of continuousJ-fractions. We obtain a meromorphic solution of regularized equations and indicate some cases where a solution can be represented in terms of rational functions. 相似文献
6.
The general construction for finding all “essentially different” nonlinearities in equations of mathematical physics is exemplified
by the inverse problem of the Grad–Shafranov equation. We present an algorithm that allows one to recover relatively fast
all essentially different sought-for nonlinear right-hand sides of the Grad–Shafranov equation. We present the first example
of a domain with smooth boundary for which the inverse problem has at most one solution in the class of affine functions,
and also in the class of exponential functions. We select some subset of simply connected domains that model, in some sense,
the so-called doublet configurations, for which the inverse problem has at least two essentially different solutions in the
class of analytic functions. In the concluding subsection of the paper, we indicate a method of recovery, from boundary data,
of all essentially different nonlinearities in equations of mathematical physics of considerably general kind, which includes
a system of equations that describes combustion and detonation processes. 相似文献
7.
We show that a Schrödinger-like differential equation for the upper spinor component, derived from the Dirac equation for a charged spinor in spherically symmetric electromagnetic potentials, can be transformed into the Schrödinger equation with some shape-invariant potentials. By choosing different electrostatic potentials and relativistic energies and also introducing new functions and changing the variables, we show that this equation transforms into the differential equations in mathematical physics. We solve these equations using the master function approach and write the spinor wave functions in terms of Rodrigues polynomials associated with these differential equations. 相似文献
8.
长水波近似方程组的新精确解 总被引:3,自引:0,他引:3
依据齐次平衡法的思想 ,首先提出了求非线性发展方程精确解的新思路 ,这种方法通过改变待定函数的次序 ,优势是使求解的复杂计算得到简化 .应用本文的思路 ,可得到某些非线性偏微分方程的新解 .其次我们给出了长水波近似方程组的一些新精确解 ,其中包括椭圆周期解 ,我们推广了有关长波近似方程的已有结果 . 相似文献
9.
We consider some triple series equations involving generalized Laguerre polynomials. These equations are reduced to triple
integral equations for Bessel functions. The closed-form solutions of the triple integral equations for Bessel functions are
obtained and, finally, we get the closed-form solutions of triple series equations for Laguerre polynomials. 相似文献
10.
Ya. I. Belopol'skaya 《Journal of Mathematical Sciences》2003,114(5):1589-1607
We derive closed equations for some nonlinear transformations of solutions to forward and backward Kolmogorov equations (which are parabolic equations with respect to measures and functions). In particular, we obtain closed equations for the logarithmic derivatives of smooth diffusion measures and for the Radon–Nikodym derivatives of a pair of absolutely continuous diffusion measures. Similar results are obtained for the backward Kolmogorov equation. Bibliography: 14 titles. 相似文献
11.
主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性. 相似文献
12.
Kazuki Okamura 《Aequationes Mathematicae》2016,90(6):1071-1085
We consider regularity for solutions of a class of de Rham’s functional equations. Under some smoothness conditions of functions making up the equation, we improve some results in Hata (Japan J Appl Math 2:381–414, 1985). Our results are applicable to some cases when the functions making up the equation are non-linear functions on an interval, specifically, polynomials and linear fractional transformations. Our results imply the singularity of some well-known singular functions, in particular, Minkowski’s question-mark function, and, some small perturbed functions of the singular functions. 相似文献
13.
In this paper, we consider a compound Poisson risk model perturbed by a Brownian motion. We construct the bivariate cumulative distribution function of the claim size and interclaim time by Farlie-Gumbel-Morgenstern copula. The integro-differential equations and the Laplace transforms for the Gerber-Shiu functions are obtained. We also show that the Gerber-Shiu functions satisfy some defective renewal equations. For exponential claims, some explicit expressions are obtained, and numerical examples for the ruin probabilities are also given. 相似文献
14.
This paper is concerned with maximization and minimization problems of the energy integral associated to p-Laplace equations depending on functions that belong to a class of rearrangements. We prove existence and uniqueness results, and present some features of optimal solutions. The radial case is discussed in detail. We also prove a result of uniqueness for a class of p-Laplace equations under non-standard assumptions. 相似文献
15.
We introduce the notion of an invariant solution relative to an involutive distribution. We give sufficient conditions for existence of such a solution to a system of differential equations. In the case of an evolution system of partial differential equations we describe how to construct auxiliary equations for functions determining differential constraints compatible with the original system. Using this theorem, we introduce linear and quasilinear defining equations which enable us to find some classes of involutive distributions, nonclassical symmetries, and differential constraints. We present examples of reductions and exact solutions to some partial differential equations stemming from applications. 相似文献
16.
Elena Barcucci Alberto Del Lungo Elisa Pergola 《Journal of Difference Equations and Applications》2013,19(4-5):435-490
In this Paper, we illustrate a method (called the ECO method) for enumerating some classes of combinatorial objects. The basic idea of this method is the following: by means of an operator that performs a "local expansion" on the objects, we give some recursive constructions of these classes. We use these constructions to deduce some new funtional equations verified by classes' generating functions. By solving the functional equations, we enumerate the combinatorial objects according to various parameters. We show some applications of the method referring to some classical combinatorial objects, such as: trees, paths, polyminoes and permutations 相似文献
17.
In this paper we present some semismooth Newton methods for solving the semi-infinite programming problem. We first reformulate the equations and nonlinear complementarity conditions derived from the problem into a system of semismooth equations by using NCP functions. Under some conditions a solution of the system of semismooth equations is a solution of the problem. Then some semismooth Newton methods are proposed for solving this system of semismooth equations. These methods are globally and superlinearly convergent. Numerical results are also given. 相似文献
18.
We recall some non-trivial, non-linear functional relations appearing in various domains of mathematics and physics, such as lattice statistical mechanics, quantum mechanics, or enumerative combinatorics. We focus, more particularly, on the analyticity properties of the solutions of these functional relations. We then consider discrete dynamical systems corresponding to birational transformations. The rational expressions for dynamical zeta functions obtained for a particular two-dimensional birational mapping, depending on two parameters, are recalled, as well as some non-trivial functional relations satisfied by these dynamical zeta functions. We finally give some functional equations corresponding to some singled out orbits of this two-dimensional birational mapping for particular values of the two parameters. This example shows that functional equations associated with curves, for real values of the variables, are actually compatible with a chaotic dynamical system. 相似文献
19.
6l.IntroductionThetheoryofWiman-Valironhasin1Portantapp1icationstodifferentiale`iuations-Wehadextendedittothemeromorpl1icf[lnctionswhichhavefinitepo1es['J.TheoremALetw(Z)=#isameromorpicfunctionwhichhavefinitepoles,andleto<3,rt},zisapointofthecircie{z:Izl=r},andlf(z)I>N(r,f)[v(r)j-1 e',thenex-certthevaluesetofrwhicl1havefinitelogarithmicmeasure,wehaveherev(r)bethecentralindexoff(z),andVl(z)=O{[v(r)j-8 '1}.1.Theorem'BLet`o(Z)asTheoremA,ltO<8`<1,zisapointofthecircle{z:lzI=r},andlf(z)l>N(r… 相似文献
20.
《Journal of Mathematical Analysis and Applications》1987,122(2):427-438
We give necessary and sufficient conditions for certain Volterra integral and integrodifferential equations in some Banach space to have a resolvent that belongs to some weighted L1-space. These conditions involve the invertibility of functions of the Laplace transforms of the kernels. 相似文献