共查询到20条相似文献，搜索用时 203 毫秒
1.
The asymptotic and oscillatory behavior of solutions of mth order damped nonlinear difference equation of the form
where m is even, is studied. Examples are included to illustrate the results. 相似文献
2.
By using the Riccati transformation and mathematical analytic methods,some sufficient conditions are obtained for oscillation of the second-order quasilinear neutral delay difference equations Δ[r n |Δz n | α-1 Δ z n ] + q n f (x n-σ)=0,where z n=x n + p n x n τ and ∞ Σ n=0 1 /r n 1/α < ∞. 相似文献
3.
In this paper, we obtain asymptotic bounds, under appropriate conditions, of solutions of third order difference equations
of the form
|
$
\Delta (p_{n - 1} \Delta (r_{n - 1} \Delta y_{n - 1} )) = f(n,y_n \Delta y_{n - 1} ) + g(n,y_n \Delta y_{n - 1} ),
$
\Delta (p_{n - 1} \Delta (r_{n - 1} \Delta y_{n - 1} )) = f(n,y_n \Delta y_{n - 1} ) + g(n,y_n \Delta y_{n - 1} ),
相似文献
4.
We obtain sufficient conditions for the Perron stability of the trivial solution of a real difference equation of the form where and. The resuits obtained are valid for the case where.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 12, pp. 1593–1603, December, 1999. 相似文献
5.
考虑含最大值项二阶中立型差分方程其中{an},{pn}和{qn}为实数列,k和■为整数且k≥1,■≥0,我们研究了方程(*)非振动解的渐近性．通过例子说明了含最大值项的方程和相应的不含最大值项方程之间的区别． 相似文献
6.
We study k
th
order systems of two rational difference equations
|
$
x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - 1} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - 1} } }}
{{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }}, y_n = \frac{{p + \sum\nolimits_{i = 1}^k {\delta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\varepsilon _i y_{n - i} } }}
{{q + \sum\nolimits_{j = 1}^k {D_j x_{n - j} + } \sum\nolimits_{j = 1}^k {E_j y_{n - j} } }} n \in \mathbb{N}
$
x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - 1} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - 1} } }}
{{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }}, y_n = \frac{{p + \sum\nolimits_{i = 1}^k {\delta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\varepsilon _i y_{n - i} } }}
{{q + \sum\nolimits_{j = 1}^k {D_j x_{n - j} + } \sum\nolimits_{j = 1}^k {E_j y_{n - j} } }} n \in \mathbb{N}
相似文献
7.
Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation
|
D( cn D( yn \text + pn yn - k ) ) + qn yn + 1 - mb = 0,n \geqslant n0 \Delta \left( {c_n \Delta \left( {y_n {\text{ + }}p_n y_n - k} \right)} \right) + q_n y_{n + 1 - m}^\beta = 0,n \geqslant n_0 相似文献
8.
We consider a new Sobolev type function space called the space with multiweighted derivatives $
W_{p,\bar \alpha }^n
$
W_{p,\bar \alpha }^n
, where $
\bar \alpha
$
\bar \alpha
= ( α
0, α
1,…, α
n
), α
i
∈ ℝ, i = 0, 1,…, n, and $
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
$
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
,
|
$
D_{\bar \alpha }^0 f(t) = t^{\alpha _0 } f(t),D_{\bar \alpha }^i f(t) = t^{\alpha _i } \frac{d}
{{dt}}D_{\bar \alpha }^{i - 1} f(t),i = 1,2,...,n
$
D_{\bar \alpha }^0 f(t) = t^{\alpha _0 } f(t),D_{\bar \alpha }^i f(t) = t^{\alpha _i } \frac{d}
{{dt}}D_{\bar \alpha }^{i - 1} f(t),i = 1,2,...,n
相似文献
9.
In this paper the authors present sufficient conditions for all bounded solutions of the second order neutral difference equation $$\Delta ^2 (y_n - py_{n - k} ) - q_n f(y_{n - \ell } ) = 0, n \in \mathbb{N}$$ to be oscillatory. Examples are provided to illustrate the results. 相似文献
10.
This work is a continuation of paper [1], where was considered analog of the problem of the first return for ultrametric diffusion.
The main result of this paper consists in construction and investigation of stochastic quantity $
\tau _{B_r (a)}
$
\tau _{B_r (a)}
( ω), which has meaning of the first passage time into domain B
r
( a) by trajectories of the Markov stochastic process ζ( t, ω).Markov stochastic process is given by distribution density f( x, t), x ∈ ℚ
p
, t ∈ R
+, which is solution of the Cauchy problem
|
$
\frac{\partial }
{{\partial t}}f(x,t) = - D_x^\alpha f(x,t),f(x,0) = \Omega (\left| x \right|_p ).
$
\frac{\partial }
{{\partial t}}f(x,t) = - D_x^\alpha f(x,t),f(x,0) = \Omega (\left| x \right|_p ).
相似文献
11.
In this paper we apply the method of potentials for studying the Dirichlet and Neumann boundary-value problems for a B-elliptic equation in the form
|
$
\Delta _{x'} u + B_{x_{p - 1} } u + x_p^{ - \alpha } \frac{\partial }
{{\partial x_p }}\left( {x_p^\alpha \frac{{\partial u}}
{{\partial x_p }}} \right) = 0
$
\Delta _{x'} u + B_{x_{p - 1} } u + x_p^{ - \alpha } \frac{\partial }
{{\partial x_p }}\left( {x_p^\alpha \frac{{\partial u}}
{{\partial x_p }}} \right) = 0
相似文献
12.
The objective of this paper is to study asymptotic properties of the third-order neutral differential equation
|
$
\left[ {a\left( t \right)\left( {\left[ {x\left( t \right) + p\left( t \right)x\left( {\sigma \left( t \right)} \right)} \right]^{\prime \prime } } \right)^\gamma } \right]^\prime + q\left( t \right)f\left( {x\left[ {\tau \left( t \right)} \right]} \right) = 0, t \geqslant t_0 . \left( E \right)
$
\left[ {a\left( t \right)\left( {\left[ {x\left( t \right) + p\left( t \right)x\left( {\sigma \left( t \right)} \right)} \right]^{\prime \prime } } \right)^\gamma } \right]^\prime + q\left( t \right)f\left( {x\left[ {\tau \left( t \right)} \right]} \right) = 0, t \geqslant t_0 . \left( E \right)
相似文献
13.
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
14.
We consider semilinear partial differential equations in ℝ
n
of the form
|
$
\sum\limits_{\frac{{|\alpha |}}
{m} + \frac{{|\beta |}}
{k} \leqslant 1} {c_{\alpha \beta } x^\beta D_x^\alpha u = F(u)} ,
$
\sum\limits_{\frac{{|\alpha |}}
{m} + \frac{{|\beta |}}
{k} \leqslant 1} {c_{\alpha \beta } x^\beta D_x^\alpha u = F(u)} ,
相似文献
15.
Zeta-generalized-Euler-constant functions,
|
$
\gamma \left( s \right): = \sum\limits_{k = 1}^\infty {\left( {\frac{1}
{{k^s }} - \int_k^{k + 1} {\frac{{dx}}
{{x^s }}} } \right)}
$
\gamma \left( s \right): = \sum\limits_{k = 1}^\infty {\left( {\frac{1}
{{k^s }} - \int_k^{k + 1} {\frac{{dx}}
{{x^s }}} } \right)}
相似文献
16.
In this paper, sufficient conditions have been obtained for oscillation of all solutions of a class of nonlinear neutral delay
difference equations of the form
|
$
\Delta \left( {r\left( n \right)\Delta \left( {y\left( n \right) + p\left( n \right)y\left( {n - m} \right)} \right)} \right) + q\left( n \right)G\left( {y\left( {n - k} \right)} \right) = 0
$
\Delta \left( {r\left( n \right)\Delta \left( {y\left( n \right) + p\left( n \right)y\left( {n - m} \right)} \right)} \right) + q\left( n \right)G\left( {y\left( {n - k} \right)} \right) = 0
相似文献
17.
§ 1 ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｄｅｌａｙｌｏｇｉｓｔｉｃｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｙｎ =ｐｎｙｎ( 1 - ｙτ(ｎ) ) ,ｎ =0 ,1 ,2 ,...,( 1 1 )ｗｈｅｒｅｐｎ ∞ｎ =0 ｉｓａｓｅｑｕｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒｅａｌｎｕｍｂｅｒｓ ,τ(ｎ) ∞ｎ =0 ｉｓａｎｏｎｄｅｃｒｅａｓｉｎｇｓｅｑｕｅｎｃｅｏｆｉｎｔｅｇｅｒｓ,τ(ｎ) <ｎａｎｄｌｉｍｎ→∞τ(ｎ) =∞ ,Δｙｎ=ｙｎ +1- ｙｎ.Ｍｏｔｉｖａｔｅｄｂｙｐｌａｕｓｉｂｌｅａｐｐｌｉｃａｔｉｏｎｓ… 相似文献
18.
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
19.
We consider a class of fourth-order nonlinear difference equations of the form
where α and β are the ratios of odd positive integers, and { p
n
} and { q
n
} are positive real sequences defined for all
satisfying the condition
We classify the nonoscillatory solutions of (Ω) and establish necessary and/or sufficient conditions for the existence of
nonoscillatory solutions with specific asymptotic behavior.
Supported by Ministry of Science, Technology and Development of Republic of Serbia – Grant No. 144003. 相似文献
20.
We study oscillatory properties of solutions of the Emden-Fowler type differential equation
|
$
u^{(n)} (t) + p(t)|u(\sigma (t))|^\lambda signu(\sigma (t)) = 0,
$
u^{(n)} (t) + p(t)|u(\sigma (t))|^\lambda signu(\sigma (t)) = 0,
相似文献
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