共查询到18条相似文献,搜索用时 46 毫秒
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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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该文研究了强制位势下非齐次拟线性薛定谔方程的多解性问题.通过山路定理和Ekeland变分原理,得到了该方程两个不同的解.所得结论是对此类拟线性方程已有结果的补充和推广. 相似文献
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本文首先应用Z2指标理论给出了一类对称泛函具有无穷多广义临界点的充分条件,进而得出了一类空间上的半线性椭圆方程具有无穷多解的结论。 相似文献
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在加权Sobolev空间中,利用Galerkin方法及推广的Brouwer定理,研究一类奇异拟线性椭圆方程高阶特征问题,得到了其非平凡弱解的存在性. 相似文献
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给出增线性椭圆方程-△u=λV(x)u+f(x.u)在Ω上的一个非零解,其中Ω
RN(N≥3)可以无界.并允许Ω=RN.V(x)可以变号,并通过截断技巧得到上述问题的一个非负解和一个非正解. 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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Existence and uniqueness results for large positive solutions are obtained for a class of quasilinear elliptic eigenvalue problems in general bounded smooth domains via a generalization of a sweeping principle of Serrin. The nonlinear terms of the problems can be negative in some intervals. The existence and structure of a mountain pass solution are also discussed. We show that this solution develops to a spike layer solution. 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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Regularity results and critical group estimates are studied for critical (p, r)-systems. Multiplicity results of solutions for a critical potential quasilinear system are also proved using Morse theory. 相似文献
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This work is devoted to studying a quasilinear elliptic boundary
value problem with superlinear nonlinearities in a weighted Sobolev
space in a domain of $\mathbb{R}^{N}$. Based on the Galerkin method,
Brouwer's theorem and the weighted compact Sobolev-type embedding
theorem, a new result about the existence of solutions is revealed
to the problem. 相似文献
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§ 1. IntroductionThepurposeofthispaperistostudytheoscillatorybehaviorofsolutionsofcertainquasi linearellipticequationsdiv( |Du|m -2 A(x)Du) + p(x) |u|m -2 u=0 ,x∈Ω Rn,(E)whereΩisanexteriordomain ,m >1 ,andfunctionsA(x) ,p(x)aretobespecifiedinthefollowingtext.Recently ,USAMI [6]consideredEq .(E)whenA(x)≡I (identitymatrix) ,andob tainedoscillationcriteriaforEq .(E)with“infiniteintegral”coefficient [cf.[6],Theorem 4].However,asfarasthepresentreferencesisconcerned ,therearefewo… 相似文献