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21.
In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations. 相似文献
22.
We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem. 相似文献
23.
B R Sitaram 《Pramana》1995,44(4):295-302
The invariants of chaotic bounded Hamiltonian systems and their relation to the solutions of the first variational equations
of the equations of motion are studied. We show that these invariants are characterized by the fact that they either lose
the property of differentiability as functions on phase space or that a certain formal power series defined in terms of the
derivatives of the invariants has zero radius of convergence. For a specific example, we show that the former possibility
appears to apply. 相似文献
24.
Marco Marletta 《Advances in Computational Mathematics》1994,2(2):155-184
This paper discusses the numerical solution of eigenvalue problems for Hamiltonian systems of ordinary differential equations.
Two new codes are presented which incorporate the algorithms described here; to the best of the author’s knowledge, these
are the first codes capable of solving numerically such general eigenvalue problems. One of these implements a new new method
of solving a differential equation whose solution is a unitary matrix. Both codes are fully documented and are written inPfort-verifiedFortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f. 相似文献
25.
J. M. Speight 《Theoretical and Mathematical Physics》2007,152(1):1043-1055
We study the dynamics of magnetic bubble solitons in a two-dimensional isotropic antiferromagnetic spin lattice in the case
where the exchange integral J(x, y) is position dependent. In the near-continuum regime, this system is described by the relativistic
O(3) sigma model on a space-time with a spatially inhomogeneous metric determined by J. We use the geodesic approximation
to describe the low-energy soliton dynamics in this system: the n-soliton motion is approximated by geodesic motion in the
moduli space M
n
of static n-solitons equipped with the L
2 metric γ. We obtain explicit formulas for γ for various natural choices of J(x, y). Based on these, we show that single soliton
trajectories are refracted with J−1 being analogous to the refractive index and that this refraction effect allows constructing simple bubble lenses and bubble
guides. We consider the case where J has a disk inhomogeneity (with the value J
+ outside a disk and J
− < J
+ inside) in detail. We argue that for sufficiently large J
+/J
−, this type of antiferromagnet supports approximate quasibreathers: two or more coincident bubbles confined within the disk
spin internally while their shape oscillates with a generically incommensurate period.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 191–208, July, 2007. 相似文献
26.
Qin Jiang 《Journal of Mathematical Analysis and Applications》2007,328(1):380-389
Some solvability conditions of periodic and subharmonic solutions are obtained for a class of subquadratic nonautonomous second-order Hamiltonian systems by the minimax methods in critical point theory. 相似文献
28.
Yi Lin 《Advances in Mathematics》2007,208(2):699-709
In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces. 相似文献
29.
Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes. 相似文献
30.
提出了将哈密顿算符对角化的一种方法.围绕一维谐振子讨论了如何将哈密顿算符对角化、引进的是玻色算符还是费米算符的问题,并分析了能量量子化的原因及能量子与声子的区别. 相似文献