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建立了H02(Ω)(0∈ΩR4)中的Hardy不等式,利用临界点理论得到了含位势的非线性双调和方程非平凡解的存在性. 相似文献
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泛函∫_ΩF(x,u,Du)dx的非平凡临界点的讨论 总被引:1,自引:0,他引:1
本文研究了泛函非平凡临界点的存在性.本文的结论的条件要比文献[1]—[4]的弱,如对泛函,条件u·g(x,u)-pG(x,u)≥-c可以取代条件u·g(x,u)-μG(x,u)≥-c,μ>p。 相似文献
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p阶平均曲率算子Dirichlet问题的无穷多个解 总被引:1,自引:0,他引:1
§ 1 IntroductionSince the Mountain Pass Theorem came out,the existence of nontrivial solutions,pos-sibly multiple,ofnonlinear elliptic equations has been extensively studied.In this paper,weconsider the following Dirichlet problem for p-(generalized) mean curvature operator:-div((1 +| u|2 ) p- 22 u) =f(x,u) , x∈Ω,u∈ W1 ,p0 (Ω ) , (1 .1 )whereΩ is a bounded domain in Rn(n>p>1 ) with smooth boundary Ω.First let us recall the following Dirichletproblem for p-Laplacian:-Δpu≡ -div… 相似文献
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本文讨论由未知函数u=0引起的下列退化变分问题正解的存在性: 证明此正解满足Harnack不等式性质,进一步讨论带自然增长退化椭圆型Euler方程具下列非齐次Dirichlet问题解的存在性: 相似文献
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In the middle of 1980s,Ni&Serrin,Grads,Ni &Nirenberg,established a generalized iueqnality for the sphelrical symmetry Solutions of quasilinear elliptic equations diV[A(|Du|)] ,f(u)=0,χ∈~n (1) By using this inequality,the results that do not exist spherical symmetry solution can be Proved.In order to study the non-existence of the nonspherical symmetry Solutions,We must establish the Pohozaev' ideutity or inequality for general nonspherical symmetry SOlutions for the most general quasilinear Euler equations 相似文献
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WEIGHTED POINCARE INEQUALITIES, ON UNBOUNDED DOMAINS AND NONLINEAR ELLIPTIC BOUNDARY VALUE, PROBLEMS
This paper is concerned with establishing Poincare type inequalities for integrals of functions and their derivatives over unbounded domains.It is well know that the Poincare inequality 相似文献
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对三维Landau-Lifshitz方程u×(-△u+λ(u,n)n)=o,|u|=1,x∈ΩR3的Dirichlet常边值问题,证明了当λ>λ1时,存在两个正则解,当λ>max(λ1,λ*)时,存在三个正则解,除常数外,还有一个是非轴对称极小解,另一个是轴对称解,其中λ1是-△算子齐次Dirichlet问题的第一特征值, 相似文献
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含临界指数的类p-Laplacian方程无穷多解的存在性 总被引:1,自引:0,他引:1
考虑如下一类含临界指数的类p-Laplacian方程-div(a(|Du|~p)|Du|~(p-2)Du)=:-- |u|~(p~*-2)u+λf(x,u),u∈W_0~(1,p)(Ω),其中Ω∈R~N(N≥2)为有界光滑区域,a:R~+→R为连续函数.由于问题失去紧性,对Palais-Smale序列的分析需要一点技巧.本文利用Lions的集中紧原理,证明了相应泛函I_λ满足(PS)_c条件,再应用Clark临界点定理和亏格的性质,证明了方程无穷多解的存在性.进一步,得到当λ充分小时一个特殊的特征函数的存在性. 相似文献