共查询到20条相似文献,搜索用时 156 毫秒
1.
Fujita型反应扩散方程组整体解的存在性、非存在性与渐近性质 总被引:5,自引:0,他引:5
本文研究 Fujita型反应扩散方程组的初值问题:ut-△u=a1u~α1-1u+b1v~β1-1v,vt-△v=a2u~α2-1u+b2v~β2-1v,u(X,0)=u0(X),V(X,0)=V0(X),(X,t)R~N x R~+,其中 ai,bi≥ 0, αi,βi≥ 1(i= 1,2),给出了非负整体 L~p解与古典解存在性与非存在性的一系列充分条件,并讨论了解的渐近性质.本文所用方法和所得结果与已有的工作[1-4],有很大的不同,不但在某些方面推广了[1-5],而且从某些方面改进了[1]的结果。 相似文献
2.
一类拟线性二阶微分方程解的振动与非振动的判定 总被引:4,自引:0,他引:4
本文讨论了拟线性微分方程(p(x'))'+q(t)p(x)=0,t≥t0,q(t)≥0(这里 p(u)=|u|p-1u,p>0是常数)的解的振动与非振动条件,并改进了文献[2]的结果. 相似文献
3.
Summary We establish new comparison theorems on the oscillation of solutions of a class of perturbed half-linear differential equations.
These improve the work of Elbert and Schneider [6] in which connections are found between half-linear differential equations
and linear differential equations. Our comparison theorems are not of Sturm type or Hille--Wintner type which are very famous.
We can apply the main results in combination with Sturm's or Hille--Wintner's comparison theorem to a half-linear differential
equation of the general form (|x'|α-1x')' + a(t) |x|α-1x = 0. 相似文献
4.
研究三维微分系统:u′1=a1(t)|u2|λ1sgn u2,u′2=a2(t)|u3|λ2sgn u3,u′3=-a3(t)|u1|λ3sgn u1.假设λi(i=1,2,3)是正的常数,ai(t)(i=1,2,3)在区间[0,∞)上是正的连续函数,根据u的分量ui的特殊渐近条件定义了正值解的几种类型。系统满足条件∫0∞ai(t)dt=∞,i=1,2. 相似文献
5.
本文给出RN(N3)中有界光滑区域Ω上的拟线性椭圆型方程:-∑Ni=1xi·|Du|p-2uxi=λ|u|p-2u+a(x)|u|p-2u+f(x,u),x∈Ω(λ>0,p=Np/(N-p),2p<N)在边界条件:-|Du|p-2Dνu|Ω=ψ(x)|u|q-2u(q=(N-1)p/(N-p))下的多解性结果. 相似文献
6.
We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping under quite general conditions. These results are extensions of the recent results developed by Sun [Y.G. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations. 相似文献
7.
关于Fujita型反应扩散方程组的Cauchy问题 总被引:5,自引:1,他引:5
本文研究Fujita型反应扩散方程组ut-Δu=α1|u|q1-1u+β1|v|p1-1v,(x∈RN,t>0),vt-Δv=α2|u|q2-1u+β2|v|p2-1v,u(x,0)=u0(x)0,v(x,0)=v0(x)0,(x∈RN)Lp解的整体存在性和有限时间Blow up问题.这里qi>1,pi>1(i=1,2),α10,α2>0,β1>0,β20,1p+∞. 相似文献
8.
马如云 《数学物理学报(A辑)》2004,24(3):307-318
设 a∈C[0,1], b∈C([0,1],(-∞, 0)). 设\-1(t)为线性边值问题
u″+a(t)u′+b(t)u=0,
u′(0)=0,\ u(1)=1
的唯一正解. 该文研究非线性二阶常微分方程m 点边值问题
u″+a(t)u′+b(t)u+h(t) f(u)=0,\=
u′(0)=0, u(1)-∑[DD(]m-2[]i=1[DD)]α\-i u(ξ\-i)=d
正解的存在性. 其中 d 为参数,
ξ\-i∈(0,1), α\-i∈(0,∞) 为满足
∑[DD(]m-2[]i=1[DD)]α\-i\-1(ξ\-i)<1的常数,
i∈{1,\:,m-2}.
在适当的条件下证得: 存在正常数 d\+*, 使
当0d\+*时无正解. 相似文献
9.
Mónica Clapp Andrzej Szulkin 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(2):229-248
We consider the magnetic nonlinear Schrödinger equations $\begin{array}{ll}{\left(-i\nabla + sA\right)^{2} u + u \, = \, |u|^{p-2}\, u, \quad p \in (2, 6),} \\ \quad \quad {\left(-i\nabla + sA\right) ^{2}u \, = \, |u|^{4}\, u,}\end{array}$ in ${\Omega=\mathcal{O}\times \mathbb{R}}We consider the magnetic nonlinear Schr?dinger equations
ll(-i?+ sA)2 u + u = |u|p-2 u, p ? (2, 6), (-i?+ sA) 2u = |u|4 u,\begin{array}{ll}{\left(-i\nabla + sA\right)^{2} u + u \, = \, |u|^{p-2}\, u, \quad p \in (2, 6),} \\ \quad \quad {\left(-i\nabla + sA\right) ^{2}u \, = \, |u|^{4}\, u,}\end{array} 相似文献
10.
11.
In this paper, we consider the complex Ginzburg-Landau equation (CGL) in three spatial dimensions u_t = ρu + (1 + iϒ
)Δu - (1 + iμ) |u|^{2σ} u, \qquad(1) u(0, x) = u_0(x), \qquad(2) where u is an unknown complex-value function defined in 3+1 dimensional space-time R^{3+1}, Δ is a Laplacian in R³, ρ > 0,
ϒ, μ are real parameters. Ω ∈ R³ is a bounded domain. We show that the semigroup S(t) associated with the problem (1), (2) satisfies Lipschitz continuity and the squeezing property for the initial-value problem (1), (2) with the initial-value condition belonging to H²(Ω ), therefore we obtain the existence of exponential attractor. 相似文献
12.
<正> 设函数 f(z)=z+a_2Z~2+…在单位圆|z|<1上是正则的单叶的.这种函数的全体形成一族 S.S 中满足条件|f(z)|
13.
研究奇异拟线性椭圆型方程{-div(|x|~(-ap)|▽u|~(p-2)▽u) + f(x)|u|~(p-2) = g(x)\u|~(q-2)u + λh(x)|u|~(r-2),x R~N,u(x) 0,x∈ R~N,其中λ0是参数,1pN(N3),1rpgp*=0a(N—p)/p,p*=Np/{N~pd),aa+l,d=a+l-60,权函数f(x),g(x),h(x)满足一定的条件.利用山路引理和Ekeland变分原理证明了问题至少有两个非平凡的弱解. 相似文献
14.
This paper is concerned with the following n-th ordinary differential equation:{u~(n)(t)=f(t,u(t),u~(1)(t),···,u~(n-1) (t)),for t∈(0,1),u~(i) (0)=0,0 ≤i≤n3,au~(n-2)(0)du~(n-1)(0)=0,cu~(n-2)(1)+du~(n-1)(1)=0,where a,c ∈ R,,≥,such that a~2 + b~2 0 and c~2+d~20,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique. 相似文献
15.
Sobolev临界增长椭圆方程注 总被引:1,自引:0,他引:1
利用空间H10(Ω)的正交分解和极小值原理给出了具临界指数2*的椭圆方程-Δu=λ1u-|u|2*-2u+g(x,u)+h(x)1解的存在性定理,这里次临界项g(x,u)关于u是非线性的,λ1为算子-Δ在H10(Ω)中最小特征值.特别当h≡0时,本文还获得了非零解的存在性结论. 相似文献
16.
利用Riccati技巧,对二阶含阻尼项椭圆型微分方程∑i,j=1N Di[aij(x)Djy]+∑i=1N bi(x)Diy+q(x)f(y)=0给出解非振动的必要条件,进而建立上述方程振动的充分准则. 相似文献
17.
Zhi Ting XU 《数学学报(英文版)》2007,23(7):1189-1198
By using vector Riccati transformation and averaging technique, some oscillation criteria for the quasilinear elliptic differential equation of second order,
ΣNi,j=1Di[Ψ(y)Aij(x)|Dy|^p-2Djy]+p(x)f(y)=0,
are obtained. These theorems extend and include earlier results for the semilinear elliptic equation and PDE with p-Laplacian. 相似文献
18.
研究了高阶线性微分方程f~(k)+A_(k-1)(z)f~(k-1)+…+A_1(z)f′+A_0(z)f=0的非零解f,及其一阶、二阶导数,f~(i)(i=1,2)的不动点性质,这里A_j(z)(j=0,1,…k-1)为亚纯函数,得到了若δ(∞,A_0)>0,且满足max{i(A1),i(A2),…,i(A_(k-1))}相似文献
19.
In this paper we are concerned with the nonlinear eigenvalue problem consisting of the functional differential equation with p -Laplacian operator, ( { p ( u '))' + u a ( t ) f ( t , u t ) = 0, { p ( s ) = | s | p m 2 s , p > 1, the initial condition, u ( s ) = } ( s ), m h s h 0, and the boundary condition, u (0) = 0 = u (1), where a ( t ) is allowed to be singular at the end points of (0, 1). Our results apply to more than just the sublinear and superlinear cases discussed in other references. 相似文献
20.
A. M. Sedletskii 《Analysis Mathematica》2002,28(1):43-60
D Ranee avtorom byli postroeny sistemy vida $$e^{-i lambda_n t} \exp (-a|t|^\alpha), \quad \lambda_n \in \Lambda; \quad a>0, \ \alpha>1,\leqno(1)$$ polnye i minimal\cprime nye v prostranstvakh $L^p ({\bf R})$ $(L^p ({\bf R}_+))$ pri $p\ge 2$. V danno\u i\ stat\cprime e stroyat\cydot sya sistemy (1), obladayushchie takim svo\u istvom v prostranstvakh $L^p({\bf R})$ $(L^p ({\bf R}_+))$, $1\le p <2$ i $C_0 ({\bf R})$ $(C_0 ({\bf R}_+))$. 相似文献
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