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101.
This paper deals with the global existence and nonexistence of solutions of the second-order nonlinear differential equation (φ(x′))′+λφ(x)=0 satisfying x(0)=x0 and x′(0)=x1, where λ is a positive parameter and φ:(−ρ,ρ)→(−σ,σ) with 0<ρ?∞ and 0<σ?∞ is strictly increasing odd bijective and continuous on (−ρ,ρ). Necessary and sufficient conditions are obtained for the initial value problem to have a unique global solution which is oscillatory and periodic. Examples are given to illustrate our main result. Finally, a nonexistence result for the equation with a damping term is discussed as an application to our result. 相似文献
102.
Multiparameter maximal estimates are considered for operators of Schrödinger type. Sharp and almost sharp results, that extend work by Rogers and Villarroya, are obtained. We provide new estimates via the integrability of the kernel which naturally appears with a TT? argument and discuss the behavior at the endpoints. We treat in particular the case of global integrability of the maximal operator on finite time for solutions to the linear Schrödinger equation and make some comments on an open problem. 相似文献
103.
Hiroshi Iritani 《Advances in Mathematics》2009,222(3):1016-595
We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the -class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for the Landau-Ginzburg model under mirror symmetry. By assuming the existence of an integral structure, we give a natural explanation for the specialization to a root of unity in Y. Ruan's crepant resolution conjecture [Yongbin Ruan, The cohomology ring of crepant resolutions of orbifolds, in: Contemp. Math., vol. 403, Amer. Math. Soc., Providence, RI, 2006, pp. 117-126]. 相似文献
104.
Weiming Ye 《Physics letters. A》2010,374(25):2521-4755
Recently, self-sustained oscillations in complex networks consisting of non-oscillatory nodes have attracted great interest in diverse natural and social fields. Oscillatory genomic regulatory networks are one of the most typical examples of this kind. Given an oscillatory genomic network, it is important to reveal the central structure generating the oscillation. However, if the network consists of large numbers of genes and interactions, the oscillation generator is deeply hidden in the complicated interactions. We apply the dominant phase-advanced driving path method proposed in Qian et al. (2010) [1] to reduce complex genomic regulatory networks to one-dimensional and unidirectionally linked network graphs where negative regulatory loops are explored to play as the central generators of the oscillations, and oscillation propagation pathways in the complex networks are clearly shown by tree branches radiating from the loops. Based on the above understanding we can control oscillations of genomic networks with high efficiency. 相似文献
105.
In this paper, the ultraviolet (UV) photorefraction effect of lithium niobate doubly doped with Ce and Mn has been investigated. It is found the diffraction efficiency shows oscillating behavior under UV-light-recording. A model based on electrons and holes as the dominant carriers is proposed to study the oscillatory behavior of the diffraction efficiency. On the basis of the material equations and the coupled-wave equations, we found that the oscillatory behavior is due to the oscillation of the relative spatial phase shift Φ. And the electron-hole competition may cause the oscillation of the relative spatial phase shift. This oscillation behavior is different from that caused by very high-strength space electric field. UV recording can suppress the beam-fanning perfectly, and the most important is the high sensitivity. 相似文献
106.
107.
Mauro Marini 《Journal of Mathematical Analysis and Applications》2004,295(2):459-472
The problem of oscillation of a second order nonlinear difference system is considered and conditions for oscillation are derived by means of a complete analysis of nonoscillatory solutions. The case of systems with deviating arguments is also analyzed, and the results are shown to significantly generalize some existing ones. 相似文献
108.
Samuel G. Dubé 《Journal of Mathematical Analysis and Applications》2005,306(1):349-363
We extend old results dealing with non-oscillations of Wintner (1951) and Opial (1957) from scalar to vector differential equations with symmetric coefficients using the Schauder fixed point theorem. 相似文献
109.
Hoang Si Nguyen Roger B. Sidje Nguyen Huu Cong 《Journal of Computational and Applied Mathematics》2007
Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge–Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge–Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. 相似文献
110.
By constructing a class of solutions to the integral inequality for t t0 large enough, where 0<A1a(τ)A2<+∞ and λ>1, that tend to zero as t→+∞ we address an open problem in the theory of nonlinear oscillations. 相似文献