共查询到20条相似文献,搜索用时 62 毫秒
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证明了各向异性泛函的极小点与各向异性方程 相似文献
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本文借助没有P.S.条件的广义越山引理证明了一类拟线性椭圆型方程在各向异性Соболев空间中的非平凡解的存在性。 相似文献
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本文借助没有P.S.条件的广义越山引理证明了一类拟线性椭圆型方程在各向异性空间中的非平凡解的存在性。 相似文献
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临界增长的椭圆型方程广义解的有界性及先验估计 总被引:1,自引:0,他引:1
本文证明了椭圆型方程由divA(x,u,u)=B(x,u,u)(在G内)在带权soblev空间中的广义解的有界性,并做出了有界解最大模的先验估计.A(x,u,ζ)和B(x,u,ζ)关于u的增长阶达到了临界指数,而且允许B(x,u,ζ)关于ζ的增长阶γ满足自然增长条件,从而推广和改进了已有的所有结果. 相似文献
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拟线性椭圆型方程的非线性边值问题——Sobolev临界指数的情形 总被引:1,自引:0,他引:1
本文讨论一类具有Sobolev临界指数的拟线性椭圆型方程非线性边值问题的非平凡解的存在性,利用集中紧原理得到一个存在性结果。 相似文献
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徐超江 《数学年刊A辑(中文版)》1994,(2)
本文研究以Hormander平方和算子为主部的半线性次椭圆型方程的Dirichlet问题的解的存在性和正则性,问题来源于所谓次椭圆几何学理论.与此同时,对于满足Hormander条件的一组向量场,我们证明了相应的Sobolev不等式.这一结果进一步的完善了Hormander平方和算子与Laplace算子的类比研究工作. 相似文献
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运用数学归纳法,Gronwall不等式及方程的守恒量等工具,研究组合KdV方程初值问题解的有界性.首先在schwartz空间得到了方程解及解的任意阶导的上确界可以由初值为变量的图灵可计算函数来控制,由于schwartz空间S(R)是Sobolev空间Hs(R)(s≥0)的稠子空间,结果可以直接推广到sobolev空间Hs(R)(s≥0),所以组合KdV方程解在Hs(R)(s≥0)上确界可以由一个可计算函数来控制,从而为研究解算子的可计算性并运用图灵机计算组合KdV方程的解奠定了基础. 相似文献
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E. I. Galakhov 《Mathematical Notes》2005,78(1-2):185-193
This paper is concerned with existence theorems for positive solutions of the Dirichlet problem for quasilinear elliptic differential equation containing a gradient term. Using the shooting method and the a priori estimates for the first zero, we obtain sufficient conditions for the existence of classical positive solutions of the problem in the ball.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 202–211.Original Russian Text Copyright © 2005 by E. I. Galakhov. 相似文献
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Darko Žubrinić 《Czechoslovak Mathematical Journal》2003,53(2):429-435
We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of p-Laplacian type. If p < < N and the right-hand side is a Radon measure with singularity of order at x0A , then any supersolution in W1,p() has singularity of order at least (–p)/(p–1) at x0. In the proof we exploit a pointwise estimate of A-superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff's potential of Radon's measure. 相似文献
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Nontrivial Solutions for Some Semilinear Elliptic Equations with Critical Sobolev Exponents
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Let Ω be a bounded domain in R^4(n ≥ 4) with smooth boundary ∂Ω. We discuss the existence of nontrivial solutions of the Dirichlet problem {- Δu = a(x) |u|^{4/(a-2)}u + λu + g(x, u), \quad x ∈ Ω u = 0, \quad x ∈ ∂Ω where a(x) is a smooth function which is nonnegative on \overline{Ω} and positive somewhere, λ> 0 and λ ∉ σ(-Δ). We weaken the conditions on a(x) that are generally assumed in other papers dealing with this problem. 相似文献
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We consider the Dirichlet problem for a class of quasilinear degenerate elliptic inclusions of the form ?div(𝒜(x, u, ?u)) + f(x)g(u) ∈ H(x, u, ?u), where 𝒜(x, u, ?u) is allowed to be degenerate. Without the general assumption that the multivalued nonlinearity is characterized by Clarke's generalized gradient of some locally Lipschitz functions, we prove the existence of bounded solutions in weighed Sobolev space with the superlinear growth imposed on the nonlinearity g and the multifunction H(x, u, ?u) by using the Leray-Schauder fixed point theorem. Furthermore, we investigate the existence of extremal solutions and prove that they are dense in the solutions of the original system. Subsequently, a quasilinear degenerate elliptic control problem is considered and the existence theorem based on the proven results is obtained. 相似文献
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本文讨论了Ω上如下一类带临界增长的椭圆方程在拟超临界的Neumann边界条件下正解的存在性:-Div(| u |p-2 u) =λum up*-1,-| u |p-2 u ν=ψ(x)uq-1,x∈Ω,x∈Ω.这里Ω∈RN,(N≥3)是光滑有界区域, 1≤p < N,0< m < p-1,(N -1)pN - p= p*N-1 ≤q < p*,其中p* =NpN - p是W1,p(Ω)→Ls(Ω)的Sobolev临界指数,p*N-1 =(N -1)pN - p是W1,p(Ω)→Lt( Ω)的在(N-1)维流形上的临界指数,λ>0是一个正参数. 相似文献
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Liang Xiting 《偏微分方程(英文版)》1991,4(3)
Under the appropriate conditions on u, the generalized solution of the elliptic equation ∫_G {∇v ⋅ A(x, u, ∇u) + vB(x, u, ∇u)}dx = 0, \quad ∀v ∈ {\WW}¹_p(G) ∩ L_∞(G) for which even the natural growth condition p(1 - 1/p^∗) < ϒ < p is permitted, the local and global boundedness of u are proved. 相似文献
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设0∈Ω∈RN,(N≥2)为有界光滑区域,利用山路定理,考虑如下一类含Hardy位势的拟线性椭圆型方程非平凡解的存在性:-△u-u△(|u|N,(N≥2)为有界光滑区域,利用山路定理,考虑如下一类含Hardy位势的拟线性椭圆型方程非平凡解的存在性:-△u-u△(|u|2)=μu/|x|2)=μu/|x|2+λg(x,u),x∈Ω,其中μ>0,λ>0为常数,g(x,u)为Caratheodory函数. 相似文献
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张辉 《应用泛函分析学报》2000,2(1):26-33
研究了方程-div(‖Du‖^-2Du)=λf(u)在R^n,n≥2中环域上的正的径向解的多重性。当f在正区域上有多个峰的情况下,我们获得了多个解。 相似文献