共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
3.
4.
5.
Miguel V.S. Frasson 《Applied mathematics and computation》2009,214(1):66-72
We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. 相似文献
6.
7.
Csaba Vincze 《Periodica Mathematica Hungarica》2017,74(1):112-117
In this paper we prove that a multivariate polynomial has algebraically dependent roots if and only if the coefficients are algebraic numbers up to a common proportional term; for the problem see section 4.4 in Varga-Vincze (On the characteristic polynomials of linear functional equations, Period Math Hungar 71(2):250–260, 2015). The case of univariate polynomials belongs to basic algebra. As far as we know the case of multivariate polynomials is not discussed in the literature. As an application we formulate a sufficient and necessary condition for the existence of non-trivial solutions of special types of linear functional equations. The criteria is based only on the algebraic properties of the parameters in the functional equation. 相似文献
8.
Konrad Schumacher 《Journal of Differential Equations》1985,59(3):355-387
We give sufficient conditions for the existence of the resolvent operator for nonautonomous linear partial differential equations with delay, where the highest order derivatives are undelayed. Furthermore we analyse the connection between the resolvent and the solution operator of the homogeneous equation. 相似文献
9.
10.
Zhi-Tao Wen Gary G. Gundersen Janne Heittokangas 《Journal of Differential Equations》2018,264(1):98-114
We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur. 相似文献
11.
《复变函数与椭圆型方程》2012,57(12):897-911
This article is devoted to considering value distribution theory of differential polynomials generated by solutions of linear differential equations in the complex plane. In particular, we consider normalized second-order differential equations f″+A(z)f=0, where A(z) is entire. Most of our results are treating the growth of such differential polynomials and the frequency of their fixed points, in the sense of iterated order. 相似文献
12.
Zalman Rubinstein 《Aequationes Mathematicae》1981,23(1):108-117
Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered. 相似文献
13.
14.
C. Brezinski 《Journal of Approximation Theory》2010,162(12):2290-2302
Let c be a linear functional defined by its moments c(xi)=ci for i=0,1,…. We proved that the nonlinear functional equations P(t)=c(P(x)P(αx+t)) and P(t)=c(P(x)P(xt)) admit polynomial solutions which are the polynomials belonging to the family of formal orthogonal polynomials with respect to a linear functional related to c. This equation relates the polynomials of the family with those of the scaled and shifted family. Other types of nonlinear functional equations whose solutions are formal orthogonal polynomials are also presented. Applications to Legendre and Chebyshev polynomials are given. Then, orthogonality with respect to a definite inner product is studied. When c is an integral functional with respect to a weight function, the preceding functional equations are nonlinear integral equations, and these results lead to new characterizations of orthogonal polynomials on the real line, on the unit circle, and, more generally, on an algebraic curve. 相似文献
15.
16.
Abbas Heydari 《Linear algebra and its applications》2010,432(2-3):661-669
We find the characteristic polynomials of adjacency and Laplacian matrices of arbitrary unweighted rooted trees in term of vertex degrees, using the concept of the rooted product of graphs. Our result generalizes a result of Rojo and Soto [O. Rojo, R. Soto, The spectra of the adjacency matrix and Laplacian matrix for some balanced trees, Linear Algebra Appl. 403 (2005) 97–117] on a special class of rooted unweighted trees, namely the trees such that their vertices in the same level have equal degrees. 相似文献
17.
18.
I. Kiguradze 《Georgian Mathematical Journal》1994,1(5):487-494
The properties of solutions of the equationu″(t) =p
1(t)u(τ1(t)) +p
2(t)u′(τ2(t)) are investigated wherep
i
:a, + ∞[→R (i=1,2) are locally summable functions τ1 :a, + ∞[→R is a measurable function, and τ2 :a, + ∞[→R is a nondecreasing locally absolutely continuous function. Moreover, τ
i
(t) ≥t (i = 1,2),p
1(t)≥0,p
2
2
(t) ≤ (4 - ɛ)τ
2
′
(t)p
1(t), ɛ =const > 0 and
. In particular, it is proved that solutions whose derivatives are square integrable on [α,+∞] form a one-dimensional linear
space and for any such solution to vanish at infinity it is necessary and sufficient that
. 相似文献
19.