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51.
52.
In this paper, the unbounded solutions for the following nonlinear planar system:
x′=a+y+−a−y−+f(t),y′=−b+x++b−x−+g(t),  相似文献   
53.
一类二阶泛函微分方程周期解存在性问题   总被引:18,自引:0,他引:18  
任景莉  葛渭高 《数学学报》2004,47(3):569-578
利用重合度理论研究一类二阶泛函微分方程x″(t)+f(t,x_t)x′~n+β(t)g(x(t-τ(t)))=p(t)的周期解问题,本文得到了周期解存在的新的结果。  相似文献   
54.
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Let I = [0, 1], c 1, c 2 ∈ (0, 1) with c 1 < c 2 and f : II be a continuous map satisfying: are both strictly increasing and is strictly decreasing. Let A = {x ∈ [0, c 1]∣f(x) = x}, a=max A, a 1 =max(A\{a}), and B = {x ∈ [c 2, 1]∣f(x) = x}, b=minB, b 1 =min(B\{b}). Then the inverse limit (I, f) is an arc if and only if one of the following three conditions holds: (1) If c 1 < f (c 1) ≤ c 2 (resp. c 1f (c 2) < c 2), then f has a single fixed point, a period two orbit, but no points of period greater than two or f has more than one fixed point but no points of other periods, furthermore, if Aφ and Bφ, then f (c 2) > a (resp. f (c 1) < b). (2) If f (c 1) ≤ c 1 (resp. f (c 2) ≥ c 2), then f has more than one fixed point, furthermore, if Bφ and A\ {a} ≠φ, f (c 2) ≥ a or if a 1 < f (c 2) < a, f 2 (c 2) > f (c 2), (resp. f has more than one fixed point, furthermore, if Aφ and B\{b}≠φ, f (c 1) ≤ b or if b < f (c 2) < b 1, f 2 (c 1) < f (c 1)). (3) If f (c 1) > c 2 and f (c 2) < c 1, then f has a single fixed point, a single period two orbit lying in I\(u, v) but no points of period greater than two, where u, v ∈ [c 1, c 2] such that f (u) = c 2 and f (v) = c 1. Supported by the National Natural Science Foundation of China (No. 19961001, No. 60334020) and Outstanding Young Scientist Research Fund. (No. 60125310)  相似文献   
57.
本文研究二阶微分方程χ"+aχ+-bχ-+f(χ)g(χ'=p(t)周期解的存在性,这里χ+=max{χ,0},χ-=max{-χ,0},a,6是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(χ)的极限lim.g(χ)=g(+∞),lim g(χ)=g(-∞)和f(χ)的极限lim,g(χ)=f(+∞),lim f(χ)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件.  相似文献   
58.
The modelling of the spread of infectious disease is carried out for time t on a measure chain T. Our approach unifies the continuous case and the discrete case . The model is described by the integral equation
where x(t) represents the proportion of the population infected at time t, f(t,x(t)) denotes the proportion of the population newly infected per unit time, and τ is the length of time an individual remains infectious. Using the measure chain calculus, we shall develop criteria for the existence of a nontrivial and nonnegative periodic solution for the modelling equation. The criteria can be implemented numerically, for this we shall give an algorithm as well as illustrative examples.  相似文献   
59.
Let be a prime congruent to 1 modulo 4, and let be rational integers such that is the fundamental unit of the real quadratic field . The Ankeny-Artin-Chowla conjecture (AAC conjecture) asserts that will not divide . This is equivalent to the assertion that will not divide , where denotes the th Bernoulli number. Although first published in 1952, this conjecture still remains unproved today. Indeed, it appears to be most difficult to prove. Even testing the conjecture can be quite challenging because of the size of the numbers ; for example, when , then both and exceed . In 1988 the AAC conjecture was verified by computer for all . In this paper we describe a new technique for testing the AAC conjecture and we provide some results of a computer run of the method for all primes up to .

  相似文献   

60.
B Ojha  P Nayak  S N Behera 《Pramana》2000,54(2):305-315
The electron-phonon interaction in the periodic Anderson model (PAM) is considered. The PAM incorporates the effect of onsite Coulomb interaction (U) between f-electrons. The influence of Coulomb correlation U on the phonon response of the system is studied by evaluating the phonon spectral function for various parameters of the model. The numerical evaluation of the spectral function is carried out in the long wavelength limit at finite temperatures keeping only linear terms in U. The observed behaviour is found to agree well with the general features obtained experimentally for some heavy fermion (HF) systems.  相似文献   
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