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 共查询到10条相似文献，搜索用时 187 毫秒
1.
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   

2.
The existence of a positive solution for the generalized predator-prey model for two species
$ \begin{gathered} \Delta u + u(a + g(u,v)) = 0in\Omega , \hfill \\ \Delta v + v(d + h(u,v)) = 0in\Omega , \hfill \\ u = v = 0on\partial \Omega , \hfill \\ \end{gathered} $ \begin{gathered} \Delta u + u(a + g(u,v)) = 0in\Omega , \hfill \\ \Delta v + v(d + h(u,v)) = 0in\Omega , \hfill \\ u = v = 0on\partial \Omega , \hfill \\ \end{gathered}   相似文献   

3.
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   

4.
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   

5.
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   

6.
A class of partial integrodifferential equation from viscoelasticity is formulated as the abstract integrodifferental equations in Banach space :
  相似文献   

7.
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   

8.
Ru Ying  XUE 《数学学报(英文版)》2010,26(12):2421-2442
we study an initial-boundary-value problem for the ＂good＂ Boussinesq equation on the half line
{δt^2u-δx^2u＋δx^4u＋δx^2u^2=0,t〉0,x〉0.
u（0,t）=h1（t）,δx^2u（0,t） =δth2（t）,
u（x,0）=f（x）,δtu（x,0）=δxh（x）.
The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data （f, h, h1, h2） belong to the product space
H^5（R^＋）×H^s-1（R^＋）×H^s/2＋1/4（R^＋）×H^s/2＋1/4（R^＋）
1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered.  相似文献   

9.
We study nonnegative solutions of the initial value problem for a weakly coupled system
  相似文献   

10.
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   

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