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 For a fixed bounded open set $Ω \subset ℝ^{N}$ , a sequence of open sets $Ω_{n} \subset Ω$ and a sequence of sets $Γ_{n} \subset \partial Ω \cap \partial Ω_{n}$ , 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 $\partial Ω_{n} ∖ Γ_{n}$ . 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 behavior of solutions of semilinear elliptic equations on an unbounded strip.

Brunovský, P., Mora, X., Poláčik, P., Solà-Morales, J. (1991)

Acta Mathematica Universitatis Comenianae. New Series

Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators

Gianni Dal Maso, François Murat (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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

Displaying 101 – 113 of 113

Applications of the bifurcation theory to evaluating critical conditions of the thermal explosion

Approximation of the resonance boundary-value problems of elliptic type with a discontinuous nonlinearity.

Approximations de type Hedberg dans les espaces $W^{m} L log L (Ω)$ et applications

Asymptotic analysis of a nonlinear partial differential equation in a semicylinder

Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent

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

Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip.

Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators

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

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

Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary

Asymptotically Linear Elliptic Boundary Value Problems.

Asymptotics for quasilinear equations with nearly critical growth.

Currently displaying 101 – 113 of 113