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Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets

Carmen Calvo-Jurado, Juan Casado-Díaz, Manuel Luna-Laynez (2009)

ESAIM: Control, Optimisation and Calculus of Variations


For a fixed bounded open set Ω N , a sequence of open sets Ω n Ω and a sequence of sets Γ n Ω Ω n , we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on Ω n , satisfying Neumann boundary conditions on Γ n and Dirichlet boundary conditions on  Ω n Γ n . We obtain a representation of the limit problem which is stable by homogenization and we prove that this representation depends on Ω n and Γ n locally.


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

Dimitri Mugnai (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant’s Nodal theorem.

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

Dimitri Mugnai (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant's Nodal theorem.

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