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11.
LI Xiong 《数学年刊B辑(英文版)》2001,22(1):31-46
51. IntroductionThe boundedness problem of solutions of the following nonlinear scalar differelltial equa-nons of second order..x f(x, t)ic g(x, t) = 0 (1'1)has been widely investigated by many authors since the 1940's, where f(x, t 1) = j(x, t),g(x, t 1) = g(x, t).When j(x, t) = 0, Equation (1.1) is a conservative system and takes the following form..x g(x, t) ~ 0. (1'2)The first contribution of the boundedness of all the solutions of Equation (1.2) is due toMorrislll, whO proved … 相似文献
12.
Hiroki Yagisita Eiji Yanagida 《Journal of Mathematical Analysis and Applications》2003,286(2):795-803
This paper is concerned with a time-periodic reaction-diffusion equation. It is known that typical trajectories approach periodic solutions with possibly longer period than that of the equation. Such solutions are called subharmonic solutions. In this paper, for any domain Ω, time-period τ>0 and integer n?2, we construct an example of a time-periodic reaction-diffusion equation on Ω with a minimal period τ which possesses a stable solution of minimal period nτ. 相似文献
13.
14.
In [14] Fernández, Heinonen and Llorente extend the Hornblower's results, about boundary behaviour of subharmonic functions in the unit disc of the complex plane, to subharmonic functions in the unit ball or the upper half space in higher dimensions. In this paper we establish that those results are also valid in the much more general setting of linear axiomatic potential theory. The interest of our general formulation relies on the applications to differential operators. We apply our result to Laplace–Beltrami operator and some uniformly elliptic second order operators in divergence form. 相似文献
15.
Benjamin G. Lorica 《Annals of Global Analysis and Geometry》1994,12(1):9-17
LetV: M be a smooth (potential) function on a compact Riemannian manifold. This gives rise to a second order Hamiltonian system. Assuming that the corresponding action functional is a Morse function, we will prove that the heat flow for subharmonics exists globally and converges to a critical point of the energy. As a Corollary, this shows the convergence of the geodesic heat flow (to a geodesic) without any curvature assumptions onM. 相似文献
16.
解析函数模的下界问题 总被引:2,自引:1,他引:1
王光 《数学物理学报(A辑)》1999,19(3):333-337
给出了在|z|<R中含有零点的解析函数的模的一个下界;其推论推广了[4]的Thm.1,由此可较易地推出[5]中关于单位圆盘上解析函数的加权代数的可除性问题的结论. 相似文献
17.
The paper presents an extended averaged equation approach to the investigation of nonlinear vibration problems. The proposed
method is applied to some free and self-excited oscillators, the Duffing's forced oscillators including main resonance, subharmonic
resonance and super harmonic resonance. The results in analyzing the vibration systems with arbitrary non-linearity show advantages
of the method. 相似文献
18.
Alexander I. Kheyfits 《分析论及其应用》2014,(1):136-140
The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n ≥ 3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0 ρ 1, then the existence of the limit limr →∞ logu(r)/N(r),where N(r) is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure. 相似文献
19.
Dual-perspective high-speed imaging and acoustic detection is used to characterise cavitation activity at the tip of a commercial 20 kHz (f0) ultrasonic horn, over 2 s sonications across the range of input powers available (20 – 100%). Imaging at 1 × 105 frames per second (fps) captures cavitation-bubble cluster oscillation at the horn-tip for the duration of the sonication. Shadowgraphic imaging at 2 Mfps, from an orthogonal perspective, probes cluster collapse and shock wave generation at higher temporal resolution, facilitating direct correlation of features within the acoustic emission data generated by the bubble activity. f0/m subharmonic collapses of the primary cavitation cluster directly beneath the tip, with m increasing through integer values at increasing input powers, are studied. Shock waves generated by periodic primary cluster collapses dominate the non-linear emissions of the cavitation noise spectra. Transitional input powers for which the value of m is indistinct, are identified. Overall shock wave content within the emission signals collected during sonications at transitional input powers are reduced, relative to input powers with distinct m. The findings are relevant for the optimisation of applications such as sonochemistry, known to be mediated by bubble collapse phenomena. 相似文献
20.
Tianqing An 《Journal of Mathematical Analysis and Applications》2007,331(1):701-711
This paper deals with the subharmonic solutions of Hamiltonian systems
(H) 相似文献