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1.
本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果 相似文献
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考虑一类具时滞的 Liénard型方程x+f[x(t) ]x(t) +g[t,x(t-τ(t) ) ]=p(t) =p(t+T) ,利用重合度理论 ,获得了此方程至少存在一个 T周期解的充分条件 相似文献
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In this paper, we establish the discrete approximation of continuous-state nonlinear branching processes in Lévy random environments by using tightness and convergence sequence in infinite dimensional product space via stochastic differential equations. Taking α-stable branching as an example, the conditions which are given to discretize continuous-state nonlinear branching processes in Lévy random environments are verified. © 2022 Chinese Academy of Sciences. All rights reserved. 相似文献
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Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD 下载免费PDF全文
The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献
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华云 《数学的实践与认识》2012,42(13):218-221
给出了二阶导数属于Lp空间时Fejér和Hermite-Hadamard型不等式的推广,得到两个新结果. 相似文献
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Chaotic motion of the dynamical system under both additive and multiplicative noise excitations 下载免费PDF全文
With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map. 相似文献
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Marc Bourdon Hervé Pajot 《Proceedings of the American Mathematical Society》1999,127(8):2315-2324
In this paper we shall show that the boundary of the hyperbolic building considered by M. Bourdon admits Poincaré type inequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner capacity estimates for some families of curves of and the fact that every quasiconformal homeomorphism is quasisymmetric. Therefore by these results, the answer to questions 19 and 20 of Heinonen and Semmes (Thirty-three YES or NO questions about mappings, measures and metrics, Conform Geom. Dyn. 1 (1997), 1-12) is NO.
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以二阶的情形讨论了Poincar差分方程y(n+m)十(a1+p1(m))y(n+m-1)+…+(an+pn(m))y(m)=0当其常系数部分x(n+m)+a1x(n+m-1)+…+anx(m)=0的特征方程有相同的根时,解的渐近性质.通过不动点方法给出了Poincar差分方程的解渐近于其常系数方程解的条件,并给出了渐近式高阶项的估计. 相似文献