Article Dans Une Revue Duke Mathematical Journal Année : 1990

Bifurcation from infinity in a nonlinear elliptic equation involving the limiting Sobolev exponent

Résumé

We consider an elliptic PDE with critical nonlinearity, and additonal subcritical and super quadratic nonlinearity, with Dirichlet boundary conditions, on a 3-dimensional smooth and bounded domain. We prove the existence of at least p+1 solutions, where p is the Ljusternik-Schnirelman category of the domain. We prove additional results concerning double peaked solutions on a ringshaped domain. In particular, we characterize the points at which the solutions blow up as the ringshaped domain becomes thinner or thicker.

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Dates et versions

hal-00943425 , version 1 (07-02-2014)

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  • HAL Id : hal-00943425 , version 1

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Olivier Rey. Bifurcation from infinity in a nonlinear elliptic equation involving the limiting Sobolev exponent. Duke Mathematical Journal, 1990, 60 (3), pp.815-861. ⟨hal-00943425⟩
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