共查询到20条相似文献,搜索用时 234 毫秒
1.
Another method for computing the densities of integrals of motion for the Korteweg-de Vries equation
B. M. Levitan 《Mathematical Notes》1977,22(1):562-565
In the first section of this article a new method for computing the densities of integrals of motion for the KdV equation is given. In the second section the variation with respect to q of the functional ∫ 0 π w (x,t,x,;q)dx (t is fixed) is computed, where W(x, t, s; q) is the Riemann function of the problem $$\begin{gathered} \frac{{\partial ^z u}}{{\partial x^2 }} - q(x)u = \frac{{\partial ^2 u}}{{\partial t^2 }} ( - \infty< x< \infty ), \hfill \\ u|_{t = 0} = f(x), \left. {\frac{{\partial u}}{{\partial t}}} \right|_{t = 0} = 0. \hfill \\ \end{gathered} $$ 相似文献
2.
In this paper, we will give some optimal estimates on the rotation number of the linear equation
$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x = 0,$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x = 0,
and that of the asymmetric equation:
$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0,$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0,
where p(t) and q(t) are almost periodic functions and
x + = max{ x,0} , x - = min{ x,0} .x_{ + } = \max \{ x,0\} ,\;x_{ - } = \min \{ x,0\} .
These estimates are obtained by introducing some kind of new norms in the spaces of almost periodic functions. 相似文献
3.
Miroslav Bartušek Mariella Cecchi Zuzana Došlá Mauro Marini 《Central European Journal of Mathematics》2011,9(1):184-195
Globally positive solutions for the third order differential equation with the damping term and delay,
$
x' + q(t)x'(t) - r(t)f(x(\phi (t))) = 0,
$
x' + q(t)x'(t) - r(t)f(x(\phi (t))) = 0,
相似文献
4.
This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form (un)t = (|ux|m-1ux)x up in (0, 1) × (0, T) subject to nonlinear boundary source (|ux|m-1ux)(1,t) = uq(1,t), (|ux|m-1ux)(0,t) = 0, and positive initial data u(x,0) = uo(x), where the parameters m, n, p, q > 0.It is proved that the problem possesses global solutions if and only if p ≤ n and q≤min{n, m(n 1)/ m 1}. 相似文献
5.
Some new oscillation criteria are established for the nonlinear damped differential equation
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