共查询到20条相似文献，搜索用时 31 毫秒
1.
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
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$\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}
$\begin{gathered}
x^{(n)} (t) = f(t,x(t),x'(t),...,x^{(n - 1)} (t)),t \in (0,1), \hfill \\
x(0) = \sum\limits_{i = 1}^m {a_i x(\xi _i ),x'(0) = ... = x^{(n - 2)} (0) = 0,x^{(n - 1)} (1) = } \sum\limits_{j = 1}^l {\beta _j x^{(n - 1)} (\eta _j )} , \hfill \\
\end{gathered}
相似文献
2.
The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for
the general elliptic equation of the second order
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$
\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
3.
This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation
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$
\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
4.
In this paper we deal with the four-point singular boundary value problem
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$
\left\{ \begin{gathered}
(\phi _p (u'(t)))' + q(t)f(t,u(t),u'(t),u'(t)) = 0,t \in (0,1), \hfill \\
u'(0) - \alpha u(\xi ) = 0,u'(1) + \beta u(\eta ) = 0, \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
(\phi _p (u'(t)))' + q(t)f(t,u(t),u'(t),u'(t)) = 0,t \in (0,1), \hfill \\
u'(0) - \alpha u(\xi ) = 0,u'(1) + \beta u(\eta ) = 0, \hfill \\
\end{gathered} \right.
相似文献
5.
The impulsive differential equation $\begin{gathered} x\prime (t) + \sum\limits_{i = 1}^m {p_i (t)x(t - \tau _i ) = 0,} {\text{ }}t \ne \xi _k , \\ \Delta x(\xi _k ) = b_k x(\xi _k ) \\ \end{gathered} $ with several retarded arguments is considered, where p i( t) ≥ 0, 1 + b k > 0 for i = 1, ..., m, t ≥ 0, $k \in \mathbb{N}$ . Sufficient conditions for the oscillation of all solutions of this equation are found. 相似文献
6.
§ 1 IntroductionIn[1 ] ,Karakostas and Tsamatos studied the existence of positive solutions for two-pointboundary value problemx″+ sign( 1 -c) q( t) f( x,x′) x′=0 ,( 1 .1 )x( 0 ) =0 ,x′( 1 ) =cx′( 0 ) ,( 1 .2 )where c∈ ( 0 ,1 )∪ ( 1 ,∞ ) .By using indices ofconvergence ofthe nonlinearity at0 and +∞and fixed point theorem in cones,they provided a priori upper and lower bounds for theslope of the solutions.The“c∈ ( 0 ,1 ) part”of their results has been extended to the fol-lowing … 相似文献
7.
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
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$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered}$\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
8.
In this paper we solve the equations |
相似文献
9.
In this paper we consider a class of nonlinear elliptic problems of the type
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$
\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.
In this paper, the sharp estimates of all homogeneous expansions for f are established, where f( z) = ( f
1( z), f
2( z), …, f
n
( z))′ is a k-fold symmetric quasi-convex mapping defined on the unit polydisk in ℂ
n
and
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$
\begin{gathered}
\frac{{D^{tk + 1} + f_p \left( 0 \right)\left( {z^{tk + 1} } \right)}}
{{\left( {tk + 1} \right)!}} = \sum\limits_{l_1 ,l_2 ,...,l_{tk + 1} = 1}^n {\left| {apl_1 l_2 ...l_{tk + 1} } \right|e^{i\tfrac{{\theta pl_1 + \theta pl_2 + ... + \theta pl_{tk + 1} }}
{{tk + 1}}} zl_1 zl_2 ...zl_{tk + 1} ,} \hfill \\
p = 1,2,...,n. \hfill \\
\end{gathered}
$
\begin{gathered}
\frac{{D^{tk + 1} + f_p \left( 0 \right)\left( {z^{tk + 1} } \right)}}
{{\left( {tk + 1} \right)!}} = \sum\limits_{l_1 ,l_2 ,...,l_{tk + 1} = 1}^n {\left| {apl_1 l_2 ...l_{tk + 1} } \right|e^{i\tfrac{{\theta pl_1 + \theta pl_2 + ... + \theta pl_{tk + 1} }}
{{tk + 1}}} zl_1 zl_2 ...zl_{tk + 1} ,} \hfill \\
p = 1,2,...,n. \hfill \\
\end{gathered}
相似文献
11.
The initial boundary value problem
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$ {*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ $ \begin{array}{*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ \end{array} 相似文献
12.
In this paper we study the first and tiie third boundary value problems for the elliptic equation
\[\begin{array}{l}
\varepsilon \left( {\sum\limits_{i,j = 1}^m {{d_{i,j}}(x)\frac{{{\partial ^2}u}}{{\partial {x_i}\partial {x_j}}} + \sum\limits_{i = 1}^m {{d_i}(x)\frac{{\partial u}}{{\partial {x_i}}} + d(x)u} } } \right) + \sum\limits_{i = 1}^m {{a_i}(x)\frac{{\partial u}}{{\partial {x_i}}} + b(x) + c} \ = f(x),x \in G(0 < \varepsilon \le 1),
\end{array}\]
as the degenerated operator bas singular points, where
\[\sum\limits_{i,j = 1}^m {{d_{i,j}}(x){\xi _i}{\xi _j}} \ge {\delta _0}\sum\limits_{i = 1}^m {\xi _i^2} ,({\delta _0} > 0,x \in G).\]
The uniformly valid asymptotic solutions of boundary value problems have been
obtained under the condition of
\[\sum\limits_{i = 1}^m {{a_i}(x){n_i}(x){|_{\partial G}} > 0,or} \sum\limits_{i = 1}^m {{a_i}(x){n_i}(x){|_{\partial G}} < 0} ,\]
where \(n = ({n_1}(x),{n_2}(x), \cdots ,{n_m}(x))\) is the interior normal to \({\partial G}\). 相似文献
13.
It is shown that the following three limits |
相似文献
14.
In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u (t) + λf (t, u) = 0, t ∈ (0, 1), u (0) = sum (biu (ξ i )) from i=1 to m-2, u(1)= sum (aiu(ξ i )) from i=1 to m-2, where λ > 0 is a parameter, 0 < ξ 1 < ξ 2 < ··· < ξ m 2 < 1 with 0 相似文献
15.
This paper concerns the study of the numerical approximation for the following initialboundary value problem
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$
\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
16.
This paper is concerned with a nonlocal hyperbolic system as follows utt = △u ＋ （∫Ωvdx ）^p for x∈R^N,t〉0 ,utt = △u ＋ （∫Ωvdx ）^q for x∈R^N,t〉0 ,u（x,0）=u0（x）,ut（x,0）=u01（x） for x∈R^N,u（x,0）=u0（x）,ut（x,0）=u01（x） for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed. 相似文献
17.
The problem of finding the asymptotic number of solutions of the system of inequalities $$\begin{gathered} \left\| {\alpha _i q} \right\|< q^{ - \sigma _i } (i = 1,...,n), \sigma _i > 0, \hfill \\ \sigma = \sum\nolimits_{i = 1}^n {\sigma _i< c(\alpha _1 ,...,\alpha _n ), q = 1,...,N,} \hfill \\ \end{gathered}$$ is solved under the assumption that for real numbers α 1,..., α n, starting from some Q=max(q 1...,q n) the inequality holds for any real λ≥0. 相似文献
18.
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
19.
We obtain sufficient conditions for the nontrivial solvability of systems of the form $$ \phi _i = b_i + \lambda _i \sum\limits_{j = 0}^\infty {a_{i - j} \phi _j ,i \in \mathbb{Z}_ + \underline{\underline {def}} \{ 0,1,2...,n,...\} ,} $$ and of the corresponding homogeneous systems. It is assumed that the sequences b = ( b 0, b 1, b 2, …) and λ = ( λ 0, λ 1, λ 2, …) and the Toeplitz matrix A = ( a i?j ) satisfy the conditions $$ \begin{gathered} a_j \geqslant 0,j \in \mathbb{Z},\sum\limits_{j = - \infty }^\infty {a_j = 1,} \sum\limits_{j = - \infty }^\infty {|j|a_j < \infty ,\sum\limits_{j = - \infty }^\infty {ja_j < 0,} } \hfill \\ b_j \geqslant 0,j \in \mathbb{Z},\sum\limits_{j = 0}^\infty {b_j = \infty ,} 1 \leqslant \lambda _i \leqslant \left( {\sum\limits_{j = - \infty }^i {a_j } } \right)^{ - 1} ,i \in \mathbb{Z}_ + . \hfill \\ \end{gathered} $$ . Under these conditions, we construct bounded solutions of homogeneous and inhomogeneous systems of the form indicated above. 相似文献
20.
Exact solutions are obtained for the first time for the half-space boundary-value problem for the vector model kinetic equations |
0, \mathop {\lim }\limits_{x \to + 0} \Psi (x,\mu ) = {\rm A}, \mu< 0, \hfill \\ \end{gathered}$$
" align="middle" vspace="20%" border="0"> 相似文献
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