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 共查询到20条相似文献，搜索用时 93 毫秒
1.
This paper is devoted to the study of the period function for a class of reversible quadratic system
$ \begin{gathered} \dot x = - 2xy, \hfill \\ \dot y = k - 1 - 2kx + \left( {k + 1} \right)x^2 - \tfrac{1} {2}y^2 . \hfill \\ \end{gathered} $ \begin{gathered} \dot x = - 2xy, \hfill \\ \dot y = k - 1 - 2kx + \left( {k + 1} \right)x^2 - \tfrac{1} {2}y^2 . \hfill \\ \end{gathered}   相似文献   

2.
It is proved that the boundary-value problem
, has a solution, provided that the following conditions are fulfilled:
, and, for ϕ(u) ≡ 0, the Galerkin method converges in the norm of the space H1(a, b; a). Several theorems of a similar kind are presented. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 246–266.  相似文献   

3.
具有脉冲的二阶三点边值问题存在性定理   总被引：2，自引：0，他引：2  
In this paper, two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses  相似文献   

4.
We consider the system
$\begin{gathered} x_{k + 1} = A_k x_k + b_k u_k , \hfill \\ u_{k + 1} = m_k^* x_k ,k = 1,2,..., \hfill \\ \end{gathered} $\begin{gathered} x_{k + 1} = A_k x_k + b_k u_k , \hfill \\ u_{k + 1} = m_k^* x_k ,k = 1,2,..., \hfill \\ \end{gathered}   相似文献   

5.
We consider the first-order Cauchy problem
$ \begin{gathered} \partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\ u|_{z = 0} = u_0 , \hfill \\ \end{gathered} $ \begin{gathered} \partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\ u|_{z = 0} = u_0 , \hfill \\ \end{gathered}   相似文献   

6.
具时滞的奇异(n-1,1)共轭边值问题的多重正解   总被引：2，自引：0，他引：2  
Abstract. This paper discusses the singular (n-l, 1) conjugate boundary value problem as fol-lows by using a fixed point index theorem in cones  相似文献   

7.
This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation
$ \left\{ \begin{gathered} x'(t) = f(t,x(t),x(\alpha _1 (t)),...,x(\alpha _n (t)))fora.e.t \in [0,T], \hfill \\ \Delta x(t_k ) = I_k (x(t_k )),k = 1,...,m, \hfill \\ x(0) = x(T). \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} x'(t) = f(t,x(t),x(\alpha _1 (t)),...,x(\alpha _n (t)))fora.e.t \in [0,T], \hfill \\ \Delta x(t_k ) = I_k (x(t_k )),k = 1,...,m, \hfill \\ x(0) = x(T). \hfill \\ \end{gathered} \right.   相似文献   

8.
The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems
$\left\{ \begin{gathered} - \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ - \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ \end{gathered} \right.$\left\{ \begin{gathered} - \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ - \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ \end{gathered} \right.  相似文献   

9.
In this paper we consider a class of nonlinear elliptic problems of the type
$ \left\{ \begin{gathered} - div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\ u = 0on\partial \Omega , \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} - div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\ u = 0on\partial \Omega , \hfill \\ \end{gathered} \right.   相似文献   

10.
We consider the three dimensional Cauchy problem for the Laplace equation uxx(x,y,z)+ uyy(x,y,z)+ uzz(x,y,z) = 0, x ∈ R,y ∈ R,0 z ≤ 1, u(x,y,0) = g(x,y), x ∈ R,y ∈ R, uz(x,y,0) = 0, x ∈ R,y ∈ R, where the data is given at z = 0 and a solution is sought in the region x,y ∈ R,0 z 1. The problem is ill-posed, the solution (if it exists) doesn't depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.  相似文献   

11.
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   

12.
The solvability of the nonlocal boundary value problem
in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle.  相似文献   

13.
Extensions of some inequalities   总被引：2，自引：0，他引：2  
Abstract. By using a simple analytic method the following inequalities are proved:  相似文献   

14.
In this paper, convex solutions for the second type of Feigenbaum’s equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.  相似文献   

15.
Necessary and sufficient conditions are derived in order that an inequality of the form
  相似文献   

16.
This paper concerns the study of the numerical approximation for the following initialboundary value problem
$ \left\{ \begin{gathered} u_t - u_{xx} = f\left( u \right), x \in \left( {0,1} \right), t \in \left( {0,T} \right), \hfill \\ u\left( {0,t} \right) = 0, u_x \left( {1,t} \right) = 0, t \in \left( {0,T} \right), \hfill \\ u\left( {x,0} \right) = u_0 \left( x \right), x \in \left[ {0,1} \right], \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} u_t - u_{xx} = f\left( u \right), x \in \left( {0,1} \right), t \in \left( {0,T} \right), \hfill \\ u\left( {0,t} \right) = 0, u_x \left( {1,t} \right) = 0, t \in \left( {0,T} \right), \hfill \\ u\left( {x,0} \right) = u_0 \left( x \right), x \in \left[ {0,1} \right], \hfill \\ \end{gathered} \right.   相似文献   

17.
We construct new families of symmetric (v, k, )-designs with parameters
  相似文献   

18.
The existence of at least one solution of the following multi-point boundary value problem
$ \left\{ \begin{gathered} [\varphi (x'(t))]' = f(t,x(t),x'(t)),t \in (0,1), \hfill \\ x(0) - \sum\limits_{i = 1}^m {\alpha _i x'(\xi _i ) = 0,} \hfill \\ x'(1) - \sum\limits_{i = 1}^m {\beta _i x(\xi _i ) = 0} \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} [\varphi (x'(t))]' = f(t,x(t),x'(t)),t \in (0,1), \hfill \\ x(0) - \sum\limits_{i = 1}^m {\alpha _i x'(\xi _i ) = 0,} \hfill \\ x'(1) - \sum\limits_{i = 1}^m {\beta _i x(\xi _i ) = 0} \hfill \\ \end{gathered} \right.   相似文献   

19.
In this paper, we use the abstract theory of semilinear parabolic equations and a priori estimate techniques to prove the global existence and uniqueness of smooth solutions to the Cauchy problem for the following system of parabolic equations:
Supported by National Science Fundation of China.  相似文献   

20.
The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system
$ \left\{ \begin{gathered} \ddot u(t) = \nabla F(t,u(t)),a.e.t \in [0,T], \hfill \\ u(0) - u(T) = \dot u(0) - \dot u(T) = 0 \hfill \\ \end{gathered} \right. $ \left\{ \begin{gathered} \ddot u(t) = \nabla F(t,u(t)),a.e.t \in [0,T], \hfill \\ u(0) - u(T) = \dot u(0) - \dot u(T) = 0 \hfill \\ \end{gathered} \right.   相似文献   

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