共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
P.G.L. Leach 《Journal of Mathematical Analysis and Applications》2003,284(1):31-48
There are seven equivalence classes of second-order ordinary differential equations possessing only three Lie point symmetries and hence not linearisible by means of a point transformation. We examine the representatives of these classes for linearisibility by means of other types of transformation. In particular we compare the potential for linearisibility and the possession of the Painlevé property. The complete symmetry group is realised in the standard algebra for each of the equivalence classes. 相似文献
3.
4.
In this paper, we study the existence of periodic solutions of the Rayleigh equations
x″+f(x′)+g(x)=e(t). 相似文献
5.
6.
7.
We study a periodic boundary-value problem for a quasilinear equation with the d'Alembert operator on the left-hand side and a nonlinear operator on the right-hand side and establish conditions under which the solution of the indicated problem is unique.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 10, pp. 1370–1375, October, 1995. 相似文献
8.
A. D. Myshkis 《Mathematical Notes》1999,66(6):719-725
Multivalued (not set-valued as in the theory of differential inclusions!) solutions of ordinary differential equations (ODE)
appear naturally in geometrical and physical problems in which the independent and dependent variablesx, y are geometric coordinates of a current point on the sought-for curve. This note contains some simple results concerning smooth
multivalued solutions of real second-order ODE resolved with respect toy″; the special role of equations of the third degree with respect toy′ is underlined. The method of investigation is based on combining ODEs fory(x) andx(y).
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 871–878, December, 1999. 相似文献
9.
10.
We carry out the classification of abelian Lie symmetry algebras of two-dimensional second-order nondegenerate quasilinear evolution equations. It is shown that such an equation is linearizable if it admits an abelian Lie symmetry algebra that is of dimension greater than or equal to 5 or of dimension greater than or equal to 3 with rank-one. 相似文献
11.
Larry Bates 《Proceedings of the American Mathematical Society》2004,132(6):1785-1786
A simple criterion for the completeness of an infinitesimal automorphism of a second-order differential equation is given.
12.
13.
14.
15.
In this paper, we give a necessary and sufficient conditions for the existence and uniqueness of periodic solutions of inhomogeneous abstract fractional differential equations with delay. The conditions are obtained in terms of R-boundedness of operator-valued Fourier multipliers determined by the abstract model. 相似文献
16.
17.
M.A.M. Alwash 《Journal of Mathematical Analysis and Applications》2007,329(2):1161-1169
For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation. 相似文献
18.
《Applied Mathematics Letters》2007,20(3):266-271
In this work, we have obtained existence results for single and multiple positive periodic solutions for a class of second-order differential equations. Our results are based on a fixed point theorem for cones. 相似文献
19.
20.
T.G Proctor 《Journal of Mathematical Analysis and Applications》1974,47(2):310-323
A variant of the Alekseev variation of constants integral equation is obtained relating the solutions of systems of the form and . For the case when f, g, and ψ have period P in t several theorems are given for the existence of periodic solutions extending known results when f is linear in x and does not depend on the parameter m-vector λ. Comparison with an older technique gives hypotheses where the method above is advantageous for establishing periodic solutions. An example is given for constructing limit cycles of autonomous second-order systems. 相似文献