共查询到20条相似文献,搜索用时 62 毫秒
1.
We study the class of nonlinear ordinary differential equations y″ y = F(z, y2), where F is a smooth function. Various ordinary differential equations with a well-known importance for applications belong to this class of nonlinear ordinary differential equations. Indeed, the Emden–Fowler equation, the Ermakov–Pinney equation, and the generalized Ermakov equations are among them. We construct Bäcklund transformations and auto-Bäcklund transformations: starting from a trivial solution, these last transformations induce the construction of a ladder of new solutions admitted by the given differential equations. Notably, the highly nonlinear structure of this class of nonlinear ordinary differential equations implies that numerical methods are very difficult to apply. 相似文献
2.
Eduardo Hernández Donal O’Regan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(5):135
We introduce a new abstract model of functional differential equations, which we call abstract degenerate neutral differential equations, and we study the existence of strict solutions. The class of problems and the technical approach introduced in this paper allow us to generalize and extend recent results on abstract neutral differential equations. Some examples on nonlinear partial neutral differential equations are presented. 相似文献
3.
D. V. Trushin 《代数通讯》2013,41(10):3594-3615
We investigate the least studied class of differential rings—the class of differential rings of nonzero characteristic. We present the notion of differentially closed quasifield and develop geometrical theory of differential equations in nonzero characteristic. The notions of quasivariety and its morphisms are scrutinized. Presented machinery is a basis for reduction modulo p for differential equations. 相似文献
4.
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of differential equations. Effective new techniques are proposed. Using these, we exhaustively describe admissible point transformations in classes of nonlinear (1+1)-dimensional Schrödinger equations, in particular, in the class of nonlinear (1+1)-dimensional Schrödinger equations with modular nonlinearities and potentials and some subclasses thereof. We then carry out a complete group classification in this class, representing it as a union of disjoint normalized subclasses and applying a combination of algebraic and compatibility methods. Moreover, we introduce the complete classification of (1+2)-dimensional cubic Schrödinger equations with potentials. The proposed approach can be applied to studying symmetry properties of a wide range of differential equations. 相似文献
5.
The approximate solution of a class of nonlinear differential equations, in the field of Mikusiński operators is constructed by using the Euler method. The obtained results are applied to a class of partial integro–differential equations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
S. G. Lobanov 《Mathematical Notes》2008,83(5-6):643-651
We justify a method for reducing a wide class of nonlinear equations (including several partial differential equations) to ordinary differential equations in locally convex spaces. The possibilities of this method are demonstrated by an example of a class of nonlinear hyperbolic partial differential equations. 相似文献
7.
It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential
equations (GODEs). In this paper, some stability concepts for retarded functional differential equations are introduced and
they are discussed using known stability results for GODEs. Then the equivalence of the different concepts of stabilities
considered here are proved and converse Lyapunov theorems for a very wide class of retarded functional differential equations
are obtained by means of the correspondence of this class of equations with GODEs.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 107–126, January, 2008. 相似文献
8.
Kei Kobayashi 《Journal of Theoretical Probability》2011,24(3):789-820
It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Itô formula is derived. When a standard Brownian motion is the original semimartingale, classical Itô stochastic differential equations driven by the Brownian motion with drift extend to a larger class of stochastic differential equations involving a time-change with continuous paths. A form of the general solution of linear equations in this new class is established, followed by consideration of some examples analogous to the classical equations. Through these examples, each coefficient of the stochastic differential equations in the new class is given meaning. The new feature is the coexistence of a usual drift term along with a term related to the time-change. 相似文献
9.
Shujun Long 《Results in Mathematics》2013,63(3-4):745-762
In this paper, a class of nonlinear stochastic neutral differential equations with delays is investigated. By using the properties of ${\mathcal{M}}$ -matrix, a differential-difference inequality is established. Basing on the differential-difference inequality, we develop a ${\mathcal{L}}$ -operator-difference inequality such that it is effective for stochastic neutral differential equations. By using the ${\mathcal{L}}$ -operator-difference inequality, we obtain the global attracting and invariant sets of nonlinear stochastic neutral differential equations with delays. In addition, we derive the sufficient condition ensuring the exponential p-stability of the zero solution of nonlinear stochastic neutral differential equations with delays. One example is presented to illustrate the effectiveness of our conclusion. 相似文献
10.
On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations 总被引:3,自引:0,他引:3
Ling-yun Gao 《应用数学学报(英文版)》2005,21(3):499-504
This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda's results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations. 相似文献
11.
In this paper, a new class of backward doubly stochastic differential equations driven by Teugels martingales associated with a Lévy process satisfying some moment condition and an independent Brownian motion is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to a class of stochastic partial differential integral equations is given. 相似文献
12.
Approximate solutions of a class of nonlinear differential equations are constructed in the field of Mikusiński operators by using a method similar to Euler's. Their character is analyzed and the error of approximation is estimated. The results are applied to a class of partial integro–differential equations. 相似文献
13.
Seiichiro Kusuoka 《Journal of Functional Analysis》2010,258(3):758-784
I considered if solutions of stochastic differential equations have their density or not when the coefficients are not Lipschitz continuous. However, when stochastic differential equations whose coefficients are not Lipschitz continuous, the solutions would not belong to Sobolev space in general. So, I prepared the class Vh which is larger than Sobolev space, and considered the relation between absolute continuity of random variables and the class Vh. The relation is associated to a theorem of N. Bouleau and F. Hirsch. Moreover, I got a sufficient condition for a solution of stochastic differential equation to belong to the class Vh, and showed that solutions of stochastic differential equations have their densities in a special case by using the class Vh. 相似文献
14.
Vahagn Aslanyan 《Archive for Mathematical Logic》2018,57(5-6):629-648
We generalise the exponential Ax–Schanuel theorem to arbitrary linear differential equations with constant coefficients. Using the analysis of the exponential differential equation by Kirby (The theory of exponential differential equations, 2006, Sel Math 15(3):445–486, 2009) and Crampin (Reducts of differentially closed fields to fields with a relation for exponentiation, 2006) we give a complete axiomatisation of the first order theories of linear differential equations and show that the generalised Ax–Schanuel inequalities are adequate for them. 相似文献
15.
16.
Differential equations have arithmetic analogues (Buium in Arithmetic differential equations, Mathematical Surveys and Monographs, vol 118. American Mathematical Society, Providence 2005) in which derivatives are replaced by Fermat quotients; these analogues are called arithmetic differential equations, and the present paper is concerned with the “linear” ones. The equations themselves were introduced in a previous paper (Buium and Dupuy, in Arithmetic differential equations on \(GL_{n}\), II: arithmetic Lie–Cartan theory, arXiv:1308.0744). In the present paper we deal with the solutions of these equations as well as with the Galois groups attached to the solutions. 相似文献
17.
G. V. Demidenko V. A. Likhoshvai T. V. Kotova Yu. E. Khropova 《Siberian Mathematical Journal》2006,47(1):45-54
We establish a connection between solutions to a broad class of large systems of ordinary differential equations and solutions to retarded differential equations. We prove that solving the Cauchy problem for systems of ordinary differential equations reduces to solving the initial value problem for a retarded differential equation as the number of equations increases unboundedly. In particular, the class of systems under consideration contains a system of differential equations which arises in modeling of multiphase synthesis. 相似文献
18.
In this paper an exact analysis of homogenous rigidly fixed vibrations of viscothermoelastic hollow sphere is presented. The basic governing partial differential equations have been reduced to ordinary differential equations by using Helmholtz decomposition equations. The uncoupled equation is taken for first class vibrations and remains independent of temperature variations, while coupled system of equations are taken for second class vibrations. Matrix Fröbenious method of extended power series has been applied in the coupled system of differential equations to get displacements and temperature. Numerical results have been presented, giving lowest frequency, dissipation factor, displacements and temperature change. 相似文献
19.
《Applied mathematics and computation》2003,134(2-3):307-317
In this paper, we generalize the well-known Liapunov-type inequality for a class of third-order differential equations without damping force to 2n+1 order differential equations. 相似文献
20.
For a class of retarded linear differential equations with solutions of exponential form, it is shown that L
p
-perturbations leave the solutions of the same form. As a particular example, the asymptotic integration of a class of differential
equations is obtained. 相似文献