Asymptotic behaviour, nodal lines and symmetry properties for
solutions of superlinear elliptic equations near  an eigenvalue

Dimitri Mugnai

Displaying similar documents to “Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue”

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

Fabricant, Alexander, Kutev, Nikolai, Rangelov, Tsviatko (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35J70, 35P15. The asymptotic of the first eigenvalue for linear second order elliptic equations in divergence form with large drift is studied. A necessary and a sufficient condition for the maximum possible rate of the first eigenvalue is proved.

Positive solution of asymptotically linear elliptic eigenvalue problems for certain differential equations of the fourth order

Jan Bochenek (1985)

Annales Polonici Mathematici

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Isolation and simplicity for the first eigenvalue of the $p$ -Laplacian with a nonlinear boundary condition.

Martínez, Sandra, Rossi, Julio D. (2002)

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A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.

Julián Fernández Bonder, Julio D. Rossi (2002)

Publicacions Matemàtiques

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In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end...

Adaptive finite element analysis based on perturbation arguments

Dai, Xiaoying, He, Lianhua, Zhou, Aihui

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We review some numerical analysis of an adaptive finite element method (AFEM) for a class of elliptic partial differential equations based on a perturbation argument. This argument makes use of the relationship between the general problem and a model problem, whose adaptive finite element analysis is existing, from which we get the convergence and the complexity of adaptive finite element methods for a nonsymmetric boundary value problem, an eigenvalue problem, a nonlinear boundary...

On semilinear elliptic eigenvalue problem with eigenparameter in the boundary conditions.

Ibrahim, S. F. M. (2002)

Southwest Journal of Pure and Applied Mathematics [electronic only]

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Eigenvalue problems of quasilinear elliptic systems on R.

Gong Bao Li (1987)

Revista Matemática Iberoamericana

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In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems -D_α (a_αβ(x,u) D_βuⁱ) + 1/2 D_uⁱ a_αβ(x,u)D_αu^j D_βu^j + h(x) uⁱ = ...

On some problems in the theory of eigenvalues and eigenfunctions associated with linear elliptic partial differential equations of the second order

Jan Bochenek (1965)

Annales Polonici Mathematici

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Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems

J. Fleckinger, J. Hernández, F. Thélin (2004)

Bollettino dell'Unione Matematica Italiana

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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.