共查询到20条相似文献,搜索用时 93 毫秒
1.
We prove the existence of cubic systems of the form $$ \begin{gathered} \dot x = y[1 - 2r(5 + 3r^2 )x + \gamma \lambda ^2 x^2 ] + a_0 x + a_1 x^2 + a_2 xy + a_3 y^2 + a_4 x^3 + a_5 x^2 y + a_6 xy^2 , \hfill \\ \dot y = - x(1 - 8rx)(1 - 3r\gamma x) - 2x[2(1 - 3r^2 ) - r\gamma (7 - 15r^2 )x]y \hfill \\ - [r(11 + r^2 ) + \gamma (1 - 22r^2 - 3r^4 )x]y^2 \hfill \\ - 2r\gamma \delta y^3 + a_0 y + a_7 x^2 + a_8 xy + a_9 y^2 + a_{10} x^3 + a_{11} x^2 y, \hfill \\ \end{gathered} $$ where α = 3r 2 + 17, γ = r 2 + 3, δ = 1 ? r 2, and λ = 3r 2 + 1, that have at least eleven limit cycles in a neighborhood of the point O(0, 0). 相似文献
2.
ZhangZhengqiu WangZhicheng 《高校应用数学学报(英文版)》2001,16(4):355-363
The sufficient condition for the existence of non-constant periodic solutions of the following planar system with four delays are obtained: 相似文献
3.
Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type
相似文献
4.
The modified Bernstein-Durrmeyer operators discussed in this paper are given byM_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt,whereWe will show,for 0<α<1 and 1≤p≤∞ 相似文献
5.
Gerhard Larcher 《manuscripta mathematica》1997,94(1):501-529
We give some “rational analoga” to metric results in the classical theory of the diophantine approximation of zero by linear forms. That is: we study the behaviour of expressions of the form $$\begin{gathered} \lim _{m \to \infty } \frac{1}{{\left| {P_s (m)} \right|}}|\{ (x_1 , \ldots ,x_s ) \in P_s (m): \hfill \\ \parallel a_1 \frac{{x_1 }}{m} + \ldots + a_s \frac{{x_s }}{m}\parallel _m \geqslant \psi (a_1 , \ldots ,a_s ,m) \hfill \\ for all - \frac{m}{2}< a_1 , \ldots ,a_s \leqslant \frac{m}{2}, \hfill \\ with (a_1 , \ldots ,a_s ) \ne (0, \ldots ,0)\} |, \hfill \\ \end{gathered} $$ whereP s (m) is a certain subset of {1, …,m} s , ψ is a certain nonnegative function, and ‖ · ‖ m means the maximum of 1/m and the distance to the nearest integer. Some of the investigations are also motivated by problems in the theory of uniform distribution and of pseudo-random number generation. The results partly depend on the validity of the generalized Riemann hypothesis. 相似文献
6.
In this article we study the abstract two parameter eigenvalue problem $$\begin{gathered} T_1 u_1 = \left( {\lambda _1 V_{11} + \lambda _2 V_{12} } \right)u_1 , \left\| {u_1 } \right\| = 1 \hfill \\ T_2 u_2 = \left( {\lambda _1 V_{21} + \lambda _2 V_{22} } \right)u_2 , \left\| {u_2 } \right\| = 1 \hfill \\ \end{gathered}$$ where, in the Hilbert spaces Hj, Tj is self-adjoint, bounded below and has compact resolvent, and Vjk are self-adjoint bounded operators, (?1)j+kVjk >> 0, j, k = 1, 2. An eigenvalue λ for this problem is a point in R2 satisfying both equations. Under appropriate conditions, the eigenvalues λn = (λ1 n, λ2 n) are countable and in R2. We aim to describe the set of limit points of λn/∥λn∥, as ∥λn∥ → ∞, in terms of the Vjk. 相似文献
7.
Essentially sharp bounds for small prime solutionsp
j
,q
i
of the following two different types of equations are obtained.
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