兰州大学机构库 >数学与统计学院
具非标准增长条件的四阶椭圆方程弱解存在性与多解性
Alternative TitleExistence and multiplicity of weak solutions for elliptic equations of forth order with nonstandard growth conditions
臧爱彬
Thesis Advisor范先令
2008-05-26
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword变指数Sobolev空间 极大函数算子 四阶椭圆方程 Cerami条件 Landau-Kolmogorov型不等式 p(x)-双调和
Abstract本文首先利用极大函数算子方法与Sobolev积分表示公式证明了变指数Lebesgue-Sobolev空间的导数插值不等式,然后应利用这些不等式证明了一个紧Sobolev 嵌入定理,并且得到了具二阶导数的Landau-Kolmogorov 型不等式和*的等价范数;在此基础上利用临界点理论分别讨论了具有Ambrosetti-Rabinowitz型增长条件以下两组四阶椭圆方程:*和*弱解的存在性与多解性。同时, 本文也讨论了不具备Ambrosetti-Rabinowitz型的增长条件上述方程弱解的存在性与多解性。
Other AbstractIn this paper, the author firstly shows the interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces by applying the maximal function operator and Sobolev integral representation,As applications, the author proves a compact Sobolev embedding theorem and a new Landau-Komogorov type inequality for the second order derivative and discusses the equivalent norms in the space * . On the base of these conclusions, the author, by the critical point theory, discusses the existence and multiplicity of the weak solutions for the following elliptic equations of fourth order with nonlinearities have the nonstandard growth conditions of Ambrosetti-Rabinowitz type respectively*and*; At the same time, the existence and multiplicity of the weak solutions for the equations as above without Ambrosetti-Rabinowitz type growth condition are discussed too.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224989
Collection数学与统计学院
Recommended Citation
GB/T 7714
臧爱彬. 具非标准增长条件的四阶椭圆方程弱解存在性与多解性[D]. 兰州. 兰州大学,2008.
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