共查询到19条相似文献,搜索用时 62 毫秒
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本文研究了下列障碍问题的非平凡解的存在性u∈K∶∫Ωu.(u-u)dx ∫Ωa(x)u.(v-u)dx∫Ωp(x,u)(v-u)dx,v∈K.其中K={v∈H01(Ω)∶vψa.e.onΩ}.利用关于不等式推广的山路引理,在a(x)和障碍p(x,ξ)满足适当的假设下,我们证明了上述不等式存在非平凡解. 相似文献
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研究非齐次椭圆方程divA(x,u,■u)=f(x)的双侧障碍问题,获得了解的局部有界性结果,这可以认为是经典结果的推广. 相似文献
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本文在一定条件下,运用Hodge分解、Sobolev嵌入定理和Lp中的Minkcwski不等式等,研究二阶拟线性椭圆型方程divA(x,u,u)=0的障碍问题很弱解的性质. 相似文献
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周轩伟 《纯粹数学与应用数学》2000,16(4):27-32,75
:建立了变分不等方程〈Au,u - v〉 + j(u) - j(v)≤〈f ,u - v〉, v∈ K的解的存在性定理 ,其中凸泛函 j(v)不必是半可加的 ,A是 j- P -强制算子 .并应用于Von Karman方程的障碍问题 . 相似文献
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设G是一个有限的简单连通图。D(G)表示V(G)的一个子集,它的每一个点至少有一个最大匹配不覆盖它。A(G)表示V(G)-D(G)的一个子集,它的每一个点至少和D(G)的一个点相邻。最后设C(G)=V(G)-A(G)-D(G)。在这篇章中,下面的被获得。⑴设u∈V(G)。若n≥1和G是n-可扩的,则(a)C(G-u)=φ和A(G-u)∪{u}是一个独立集,(b)G的每个完美匹配包含D(G-u)的每个分支的一个几乎守美匹配,并且它匹配A(G-u)∪{u}的所有点与D(G-4)的不同分支的点。⑵若G是2-可扩的,则对于u∈V(G),A(G-u)∪{u}是G的一个最大障碍且G的最大障碍的个数是2或是│V(G)│.⑶设X=Cay(Q,S),则对于u∈Q,(a)A(X-u)=φ=C(G-u)和X-u是一个因子临界图,或(b)C(X-u)=φ和X的两部是A(X-u)∪{u}和D(X-u)且│A(X-u)∪{u}│=│D(X-u)│。⑷设X=Cay(Q,S),则对于u∈Q,A(X-u)∪{u}是X的一个最大障碍且X的最大障碍的个数是2或是│Q│。 相似文献
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金永阳 《数学物理学报(A辑)》2009,29(5):1434-1441
该文得到了在Ω上以下问题
{Lp,ku+f(u)=0, ,
u|∂Ω=0
非负解的不存在性结果. 其中Ω为Heisenberg型群G中的区域(有界或无界), Lp, ku=divX (| X u|p-2 X u)为对应于Greiner型向量场 X 的一类次P-Laplace算子. 相似文献
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Using the method of balancing arguments, large time asymptotic behaviors for the periodic solutions of generalized Burgers equations ut + u 3 ux + ju /2 t =δ/2 uxx and ut + u 3 ux +λ u =δ/2 uxx subject to the periodic initial condition and the vanishing boundary conditions u (0, t ) = u ( l , t ) = 0, t ≥ 0 or t 0 , where A , A 1 , δ, λ, l , t 0 , ∈ R + and j = 1, 2 , are obtained. 相似文献
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We consider ut = u α uxxx + n ( u ) ux uxx + m ( u ) u 3 x + r ( u ) uxx + p ( u ) u 2 x + q ( u ) ux + s ( u ) with α= 0 and α= 3 , for those functional forms of m , n , p , q , r , s for which the equation is integrable in the sense of an infinite number of Lie-Bäcklund symmetries. Recursion operators which are x - and t -independent that generate these infinite sets of (local) symmetries are obtained for the equations. A combination of potential forms, hodograph transformations, and x -generalized hodograph transformations are applied to the obtained equations. 相似文献
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该文讨论了下列拟线性椭圆方程的Dirichlet问题在一类Orlicz-Sobolev 空间中非平凡解的存在性
{ -div(a(| u(x)|) u(x))=g(x, u), x∈Ω,
u(x)=0,x∈∂Ω.
其中Ω 是 Rn 中光滑的有界区域.Φ 和 g 满足一定条件时, 利用推广的山路引理证明了上述Dirichlet 问题存在广义的非平凡解的存在性. 相似文献
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We prove that arbitrary (nonpolynomial) scalar evolution equations of order m ≥ 7 , that are integrable in the sense of admitting the canonical conserved densities ρ(1) , ρ(2) , and ρ(3) introduced in [ 1 ], are polynomial in the derivatives u m − i for i = 0, 1, 2. We also introduce a grading in the algebra of polynomials in u k with k ≥ m − 2 over the ring of functions in x , t , u , … , u m −3 and show that integrable equations are scale homogeneous with respect to this grading . 相似文献
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通过建立Heisenberg群上无穷远处的集中列紧原理, 研究了如下$p$ -次Laplace方程
-ΔH, pu=λg(ξ)|u|q-2u+f (ξ)|u|p*-2u,在Hn上,
u∈ D1, p(Hn),
其中ξ∈Hn,λ∈R,1
j, 且m, j为整数. 相似文献
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Asymptotic formulas, as ɛ→ 0+ , are derived for the solutions of the nonlinear differential equation ɛ u" + Q ( u ) = 0 with boundary conditions u (-1) = u (1) = 0 or u '(-1) = u '(1) = 0 . The nonlinear term Q ( u ) behaves like a cubic; it vanishes at s - , 0, s + and nowhere else in [ s - , s + ] , where s - < 0 < s + . Furthermore, Q '( s ± ) < 0, Q '(0) > 0 and the integral of Q on the interval [ s - , s + ] is zero. Solutions to these boundary-value problems are shown to exhibit internal shock layers, and the error terms in the asymptotic approximations are demonstrated to be exponentially small. Estimates are obtained for the number of internal shocks that a solution can have, and the total numbers of solutions to these problems are also given. All results here are established rigorously in the mathematical sense. 相似文献
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该文主要讨论了如下p(x)-Laplacian算子方程的解.其中1P-≤p(x)≤P+N.得到了上述方程在变指数Sobolev空间W~(1,p(x))(R~N)中的一列能量值趋向正无穷的解. 相似文献
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We study characteristic Cauchy problems for the Korteweg–de Vries (KdV) equation ut = uux + uxxx , and the Kadomtsev–Petviashvili (KP) equation uyy =( uxxx + uux + ut ) x with holomorphic initial data possessing non-negative Taylor coefficients around the origin. For the KdV equation with initial value u (0, x )= u 0 ( x ), we show that there is no solution holomorphic in any neighborhood of ( t , x )=(0, 0) in C2 unless u 0 ( x )= a 0 + a 1 x . This also furnishes a nonexistence result for a class of y -independent solutions of the KP equation. We extend this to y -dependent cases by considering initial values given at y =0, u ( t , x , 0)= u 0 ( x , t ), uy ( t , x , 0)= u 1 ( x , t ), where the Taylor coefficients of u 0 and u 1 around t =0, x =0 are assumed non-negative. We prove that there is no holomorphic solution around the origin in C3 , unless u 0 and u 1 are polynomials of degree 2 or lower. MSC 2000: 35Q53, 35B30, 35C10. 相似文献