共查询到20条相似文献,搜索用时 15 毫秒
1.
Luis T Magalhães 《Journal of Differential Equations》1984,54(3):310-345
The existence of “slow” and “fast” manifolds, and of invariant manifolds approaching the manifold of orbits of the degenerate system, is discussed for singularly perturbed systems of linear retarded functional differential equations (FDE). It is shown that these manifolds exist only in very degenerate situations and, consequently, the geometry of the flow of singularly perturbed ordinary differential equations does not generalize to FDEs. 相似文献
2.
Conclusions If the defining equation corresponding to the number k0<0 has a multiple root
0(t)
, then Theorem I is inapplicable. In this case to find particular solutions of (I) one should, with the help of the substitution (t)=k
00(t)+(t) pass to an equation for (t) and investigate it by the method of Newton's diagram.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 37, No. 6, pp. 695–702, November–December, 1985. 相似文献
3.
We study the singularly perturbed state-dependent delay-differential equation
(?) 相似文献
4.
Jack K. Hale Wenzhang Huang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(1):57-88
We consider a general class of singularly perturbed delay differential systems depending on a singular parameter and another parameter . For =0, the equation defines a mapT which undergoes a generic period doubling at =0. If the bifurcation is supercritical (subcritical), these period two points define a stable period two square wave (unstable period two pulse wave). We give conditions on the vector field such that there is a sectorS in the , plane such that there is a unique periodic orbit if the parameters are inS, the orbit is stable (unstable) if the period doubling bifurcation is supercritical (subcritical) and approaches the square (pulse) wave as 0.Partially supported by NSF and DARPA. 相似文献
5.
K. I. Chernyshov 《Journal of Mathematical Sciences》1992,62(6):3153-3164
Asymptotic expansions are constructed for the general solution of a finitedimensional singularly perturbed linear differential equation in cases of strong degeneracy of the structure matrix. For additional restrictions on the elements of the structure matrix these cases can be reduced to the case when the new structure matrix is nondegenerate.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR, Vol. 195, pp. 161–178, 1991.The author deeply thanks S. G. Krein, A. P. Oskolov, and V. M. Babich for useful discussions. 相似文献
6.
In this paper, we consider the multiplicity of positive solutions for a class of singular higher-order perturbed differential systems with different orders. By employing a well-known fixed point theorem, some new existence results are given under the case where nonlinearity can be sign changing. 相似文献
7.
G. Z. Zhukova 《Ukrainian Mathematical Journal》1990,42(10):1262-1266
Solutions with asymptotics in integral and fractional powers of the parameter ? are constructed for the vector differential equation $$\varepsilon ^h \dot X = A(t,\varepsilon ) X + \varepsilon ^{\alpha _1 } p(t,\varepsilon ) \exp \left( {\varepsilon ^{ - h} \int\limits_0^t {\lambda (\tau )d\tau } } \right)$$ in the case of resonance and multiple spectrum of the limit matrix. $$\varepsilon ^h \dot X = A(t,\varepsilon ) X + \varepsilon ^{\alpha _1 } p(t,\varepsilon ) \exp \left( {\varepsilon ^{ - h} \int\limits_0^t {\lambda (\tau )d\tau } } \right)$$ 相似文献
8.
9.
K. Nipp 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1985,36(2):309-320
For singularly perturbed systems of ODE's satisfying a certain stability assumption the existence of an asymptotically stable (unstable) invariant manifold is proved. This invariant manifold is -close to the so-called reduced manifold of such a system. As an illustrative example a 3-dimensional autonomous system describing a model in biochemistry is considered.
Zusammenfassung Für singulär gestörte Differentialgleichungssysteme, die einer gewissen Stabilitätsbedingung genügen, wird die Existenz einer asymptotisch stabilen (instabilen) invarianten Mannigfaltigkeit nachgewiesen, die in einer -Umgebung der sogenannten reduzierten Mannigfaltigkeit eines solchen Systems liegt. Als Anschauungsbeispiel wird ein dreidimensionales autonomes System betrachtet, welches ein biochemisches Modell beschreibt.相似文献
10.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 652–658, May, 1989. 相似文献
11.
Andrea Malchiodi 《Frontiers of Mathematics in China》2008,3(2):239-252
We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic
behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.
相似文献
12.
F. A. Rihan 《Computational Mathematics and Modeling》2008,19(3):292-303
Singular perturbation problems containing a small positive parameter ε occur in many areas, including biochemical kinetics, genetics, plasma physics, and mechanical and electrical systems. A uniformly
valid, reliable interpretable approximation of such problems is required. This paper provides sufficient conditions to ensure
the exponential stability of the analytical and numerical solutions of the singularly perturbed delay differential equations
with a bounded time-lag for suf.ciently small ε > 0. The Halanay inequality is used to prove the main results of the paper. A numerical example is provided to illustrate
the methodology and clarify the need for a stiff solver for numerical solutions of these problems. 相似文献
13.
The oscillation of perturbed functional differential equations 总被引:1,自引:0,他引:1
We provide new oscillation criteria for the perturbed functional differential equations. This solves some open problems of [1]. An application to an equation arising in nonlinear neural networks is illustrated. 相似文献
14.
In this paper, the exponential stability of singularly perturbed impulsive delay differential equations (SPIDDEs) is concerned. We first establish a delay differential inequality, which is useful to deal with the stability of SPIDDEs, and then by the obtained inequality, a sufficient condition is provided to ensure that any solution of SPIDDEs is exponentially stable for sufficiently small ε>0. A numerical example and the simulation result show the effectiveness of our theoretical result. 相似文献
15.
16.
In this work, a singularly perturbed second-order ordinary differential equation is solved by applying a new Liouville–Green transform and the asymptotic solutions are obtained. As an application, we employ our results in discussing a second-order multi-point boundary value problem. 相似文献
17.
鲁世平 《高校应用数学学报(英文版)》2000,15(2):137-142
Abstract. In this paper,a kind of boundary value problems for Volterra functional differential e-quation is studied. 相似文献
18.
Juncheng Wei 《manuscripta mathematica》1998,96(1):113-131
We obtain necessary conditions for the existence of two-peaked solutions of singularly perturbed elliptic equations. These
conditions are related to the geometry of the domain. In particular, we prove there are no two-peaked solutions in a strictly
convex domain.
Received: 20 January 1997 / Revised version: 2 December 1997 相似文献
19.
20.
A. B. Vasil’eva 《Ukrainian Mathematical Journal》2007,59(3):396-408
We present results from the theory of singular perturbations and, in particular, from a new branch of this theory (contrast
alternating-type structures).
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 3, pp. 359–369, March, 2007. 相似文献