共查询到20条相似文献,搜索用时 11 毫秒
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GaoLingyun 《高校应用数学学报(英文版)》2005,20(1):45-50
Using value distribution theory and techniques,the problem of the algebroid solutions of second order algebraic differential equation is investigated. Examples show that the results are sharp. 相似文献
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O. V. Kaptsov 《Theoretical and Mathematical Physics》2016,189(2):1592-1608
We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds. 相似文献
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Zenonas Navickas Liepa Bikulciene Maido Rahula Minvydas Ragulskis 《Communications in Nonlinear Science & Numerical Simulation》2013,18(6):1374-1389
Solutions of the KdV equation are derived by the algebraic operator method based on generalized operators of differentiation. The algebraic operator method based on the generalized operator of differentiation is exploited for the derivation of analytic solutions to the KdV equation. The structure of solitary solutions and explicit conditions of existence of these solutions in the subspace of initial conditions are derived. It is shown that special solitary solutions exist only on a line in the parameter plane of initial and boundary conditions. This new theoretical result may lead to important findings in a variety of practical applications. 相似文献
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C. Sophocleous P. G. L. Leach K. Andriopoulos 《Mathematical Methods in the Applied Sciences》2008,31(6):679-694
Schwartz (J. Finance 1997; 52 :923–973) presented three models for the pricing of a commodity. The simplest was a variation on the Black–Scholes equation. The second allowed for a stochastic convenience yield on the commodity and the third added a stochastic variation in the underlying interest rate. We apply the techniques of Lie group analysis to resolve these equations, discuss their peculiar algebraic properties and indicate the route to the addition of other stochastic influences. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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W.M Oliva 《Journal of Differential Equations》1983,49(3):453-472
Using a Poincaré compactification, the linear homogeneous system of delay equations {x = Ax(t ? 1) (A is an n × n real matrix) induces a delay system π(A) on the sphere Sn. The points at infinity belong to an invariant submanifold Sn ? 1 of Sn. For an open and dense set of 2 × 2 matrices A with distinct eigenvalues, the system π(A) has only hyperbolic critical points (including the critical points at infinity). For an open and dense set of 2 × 2matrices with complex eigenvalues, the nonwandering set at infinity is the union of an odd number of hyperbolic periodic orbits; if , the restriction of to S1 is Morse-Smale. For n = 1 there exist periodic orbits of period 4 provided that and Hopf bifurcation of a center occurs for ?A near . 相似文献
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Symmetries of the first integrals for scalar linear or linearizable secondorder ordinary di?erential equations (ODEs) have already been derived and shown to exhibit interesting properties. One of these is that the symmetry algebra sl(3, IR) is generated by the three triplets of symmetries of the functionally independent first integrals and its quotient. In this paper, we first investigate the Lie-like operators of the basic first integrals for the linearizable maximally symmetric system of two second-order ODEs represented by the free particle system, obtainable from a complex scalar free particle equation, by splitting the corresponding complex basic first integrals and its quotient as well as their associated symmetries. It is proved that the 14 Lie-like operators corresponding to the complex split of the symmetries of the functionally independent first integrals I1, I2 and their quotient I2/I1 are precisely the Lie-like operators corresponding to the complex split of the symmetries of the scalar free particle equation in the complex domain. Then, it is shown that there are distinguished four symmetries of each of the four basic integrals and their quotients of the two-dimensional free particle system which constitute four-dimensional Lie algebras which are isomorphic to each other and generate the full symmetry algebra sl(4, IR) of the free particle system. It is further shown that the (n + 2)-dimensional algebras of the n + 2 first integrals of the system of n free particle equations are isomorphic to each other and generate the full symmetry algebra sl(n + 2, IR) of the free particle system. 相似文献
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Zusammenfassung In dieser Arbeit werden Ausdrücke für das Verschiebungsfeld in einer elastischen Kugel angegeben, deren Oberfläche a) elastisch gelagert, b) eingespannt, c) frei ist. Die Verschiebungen werden durch diejenigen Verschiebungen und Spannungen ausgedrückt, die in einem unendlichen Körper unter derselben Verteilung von Singularitäten entstehen. 相似文献
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The equationbelongs to the class of linear functional equations. The solutions form a linear space with respect to the usual pointwise operations. According to the classical results of the theory they must be generalized polynomials. New investigations have been started a few years ago. They clarified that the existence of non-trivial solutions depends on the algebraic properties of some related families of parameters. The problem is to find the necessary and sufficient conditions for the existence of non-trivial solutions in terms of these kinds of properties. One of the earliest results is due to Z. Daróczy [1]. It can be considered as the solution of the problem in case of n = 2. We are going to take more steps forward by solving the problem in case of n = 3.
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$$\sum^{n}_ {i=0} a_{i}f(b_{i}x + (1 - b_{i})y) = 0$$
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In a previous paper a preconditioning strategy based on overlapping domain decomposition was applied to the Galerkin approximation
of elliptic partial differential equations on the sphere. In this paper the methods are extended to more general pseudodifferential
equations on the sphere, using as before spherical radial basis functions for the approximation space, and again preconditioning
the ill-conditioned linear systems of the Galerkin approximation by the additive Schwarz method. Numerical results are presented
for the case of hypersingular and weakly singular integral operators on the sphere
\mathbbS2{\mathbb{S}^2} . 相似文献