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Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations

Qin Li, Qun Lin, Hehu Xie (2013)

Applications of Mathematics

The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, Q 1 rot , E Q 1 rot and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to...

Non-existence result for quasi-linear elliptic equations with supercritical growth

Zuo Dong Yang, Junli Yuan (2007)

Commentationes Mathematicae Universitatis Carolinae

We obtain a non-existence result for a class of quasi-linear eigenvalue problems when a parameter is small. By using Pohozaev identity and some comparison arguments, non-existence theorems are established for quasi-linear eigenvalue problems under supercritical growth condition.

Nonlinear homogeneous eigenvalue problem in R N : nonstandard variational approach

Pavel Drábek, Zakaria Moudan, Abdelfettah Touzani (1997)

Commentationes Mathematicae Universitatis Carolinae

The nonlinear eigenvalue problem for p-Laplacian - div ( a ( x ) | u | p - 2 u ) = λ g ( x ) | u | p - 2 u in N , u > 0 in N , lim | x | u ( x ) = 0 , is considered. We assume that 1 < p < N and that g is indefinite weight function. The existence and C 1 , α -regularity of the weak solution is proved.

Non-local Gel'fand problem in higher dimensions

Tosiya Miyasita, Takashi Suzuki (2004)

Banach Center Publications

The non-local Gel’fand problem, Δ v + λ e v / Ω e v d x = 0 with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.

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