共查询到20条相似文献,搜索用时 15 毫秒
1.
该文研究具有正负系数的非线性中立型脉冲时滞微分方程获得了该方程的每一个解当t→∞时趋于一个常数的充分条件. 相似文献
2.
On Initial-boundary-value Problems for a Class of Systems of Quasi-linear Evolution Equations 下载免费PDF全文
Cheng Yan 《偏微分方程(英文版)》1994,7(4)
In this paper the initial-boundary-value problems for pseudo-hyperbolic system of quasi-linear equations: {(-1)^Mu_{tt} + A(x, t, U, V)u_x^{2M}_{tt} = B(x, t, U, V)u_x^{2M}_{t} + C(x, t, U, V)u_x^{2M} + f(x, t, U, V) u_x^k(0,t) = ψ_{0k}(t), \quad u_x^k(l,t) = ψ_{lk}(t), \quad k = 0,1,…,M - 1 -u(x,0) = φ_0(x), \quad u_t(x,0) = φ_1(x) is studied, where U = (u_1, u_x,…,u_x^{2M - 1}) V = (u_t, u_{xt},…,u_x^{2M - 1_t}), A, B, C are m × m matrices, u, f, ψ_{0k}, ψ_{1k}, ψ_0, ψ_1 are m-dimensional vector functions. The existence and uniqueness of the generalized solution (in H² (0, T; H^{2M} (0, 1))) of the problems are proved. 相似文献
3.
Bitao Cheng Xian Wu Jun Liu 《NoDEA : Nonlinear Differential Equations and Applications》2012,19(5):521-537
In the present paper, by applying variant mountain pass theorem and Ekeland variational principle we study the existence of multiple nontrivial solutions for a class of Kirchhoff type problems with concave nonlinearity $$ \left\{\begin{array}{ll} -(a + b \int\nolimits_{\Omega} |\nabla{u}|^{2})\triangle{u} = \alpha(x)|u|^{q-2}u + f(x, u),\quad{\rm in}\;\Omega,\\ u = 0,\;\quad\qquad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad{\rm on}\;\partial\Omega, \end{array} \right. $$ A new existence theorem and an interesting corollary of four nontrivial solutions are obtained. 相似文献
4.
Junjie Li 《Mathematische Annalen》2007,339(2):251-285
We are concerned with existence, positivity property and long-time behavior of solutions to the following initial boundary
value problem of a fourth order degenerate parabolic equation in higher space dimensions 相似文献
5.
In this paper we prove existence and comparison results for nonlinear parabolic equations which are modeled on the problem
$\left\{{ll}{u_t - {\rm div}\,\left(\frac{1}{(1+|u|)^{\alpha}}|Du|^{p-2}Du\right)
=f\quad\hskip 2pt \,\,{\rm in}\,\Omega\times(0,T),}\\
{u=0\qquad\qquad\qquad\qquad\quad\quad\qquad{\rm
on}\,\partial\Omega\times(0,T),}\\
{u(x,0)=u_0(x)\quad\qquad\qquad\qquad\qquad{\rm
in}\,\Omega,}\right.$\left\{\begin{array}{ll}{u_t - {\rm div}\,\left(\frac{1}{(1+|u|)^{\alpha}}|Du|^{p-2}Du\right)
=f\quad\hskip 2pt \,\,{\rm in}\,\Omega\times(0,T),}\\
{u=0\qquad\qquad\qquad\qquad\quad\quad\qquad{\rm
on}\,\partial\Omega\times(0,T),}\\
{u(x,0)=u_0(x)\quad\qquad\qquad\qquad\qquad{\rm
in}\,\Omega,}\end{array}\right. 相似文献
6.
Fujita exponents for evolution problems with nonlocal diffusion 总被引:1,自引:0,他引:1
We prove the existence of a critical exponent of Fujita type for the nonlocal diffusion problem
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