|
$
\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
2.
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
3.
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
4.
We study the existence of a solution to the nonlinear fourth-order elastic beam equation with nonhomogeneous boundary conditions
|
$\left\{ \begin{gathered}
u^{(4)} (t) = f(t,u(t),u'(t),u'(t),u'(t)),a.e.t \in [0,1], \hfill \\
u(0) = a,u'(0) = b,u(1) = c,u'(1) = d, \hfill \\
\end{gathered} \right.
$\left\{ \begin{gathered}
u^{(4)} (t) = f(t,u(t),u'(t),u'(t),u'(t)),a.e.t \in [0,1], \hfill \\
u(0) = a,u'(0) = b,u(1) = c,u'(1) = d, \hfill \\
\end{gathered} \right.
相似文献
5.
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
6.
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
7.
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
8.
The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN:{■tu-xu + b ·▽xu + au + V(t,x)v = Hv(t,x,u,v),-■tv-xv-b·▽xv + av + V(t,x)u = Hu(t,x,u,v),where z =(u,v):R × RN → Rm × Rm,a > 0,b =(b1,···,bN) is a constant vector and V ∈ C(R × RN,R),H ∈ C1(R × RN × R2m,R).Under suitable conditions on V(t,x) and the nonlinearity for H(t,x,z),at least one non-stationary homoclinic solution with least energy is obtained. 相似文献
9.
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
10.
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
11.
Using the Leggett-Williams fixed point theorem,we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u(t)+g(t)f(t,u(t))=0,0 相似文献
12.
The singular boundary value problems of third-order differential equations
|
$
{*{20}c}
{ - u'(t) = h(t)f(t,u(t)), t \in (0,1),} \\
{u(0) = u'(0) = 0, u'(1) = \alpha u'(\eta )} \\
$
\begin{array}{*{20}c}
{ - u'(t) = h(t)f(t,u(t)), t \in (0,1),} \\
{u(0) = u'(0) = 0, u'(1) = \alpha u'(\eta )} \\
\end{array}
相似文献
13.
In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\left\{ \begin{gathered} (\phi _p (u\prime ))\prime + q(t)f(t, u) = 0,0< t< 1, \hfill \\ u(0) - B(u\prime (\eta )) = 0, u\prime (1) = 0 \hfill \\ \end{gathered} \right.$$ and $$\left\{ \begin{gathered} (\phi _p (u\prime ))\prime + q(t)f(t, u) = 0,0< t< 1, \hfill \\ u\prime (0) = 0, u(1) + B(u\prime (\eta )) = 0 \hfill \\ \end{gathered} \right.$$ The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0,1. 相似文献
14.
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
15.
Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point
boundary value problem at resonance
|
$\begin{gathered}
x^{(n)} (t) = f(t,x(t),x'(t),...,x^{(n - 1)} (t)),t \in (0,1), \hfill \\
x(0) = \sum\limits_{i = 1}^m {a_i x(\xi _i ),x'(0) = ... = x^{(n - 2)} (0) = 0,x^{(n - 1)} (1) = } \sum\limits_{j = 1}^l {\beta _j x^{(n - 1)} (\eta _j )} , \hfill \\
\end{gathered}
$\begin{gathered}
x^{(n)} (t) = f(t,x(t),x'(t),...,x^{(n - 1)} (t)),t \in (0,1), \hfill \\
x(0) = \sum\limits_{i = 1}^m {a_i x(\xi _i ),x'(0) = ... = x^{(n - 2)} (0) = 0,x^{(n - 1)} (1) = } \sum\limits_{j = 1}^l {\beta _j x^{(n - 1)} (\eta _j )} , \hfill \\
\end{gathered}
相似文献
16.
This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian： {（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0, where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given. 相似文献
17.
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
18.
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
19.
The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for
the general elliptic equation of the second order
|
$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
相似文献
20.
Let Θ = ( θ
1, θ
2, θ
3) ∈ ℝ 3. Suppose that 1, θ
1, θ
2, θ
3 are linearly independent over ℤ. For Diophantine exponents
|
$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered}$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered} 相似文献
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