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Title
Instability of saddle solutions of semilinear elliptic equations

Abstract

In a joint work with Xavier Cabre, we study the instability properties of some saddle solutions of the semilinear elliptic equations $-\Delta u=u-u^3$ in the whole $\R^{2m}$.

In 1995 M. Schatzman proved that in dimension $2$ there exists a saddle solution and it is unstable.

We prove that saddle solutions exist for every even dimension and that such solutions are unstable in dimension $4$. Furthermore, we establish that every solution vanishing on the Simons cone is unstable in dimension $4$.

Speaker(s)
Joana Terra (Universitat Politecnica de Catalunya)

Date
December 02, 2005

Time
14h 30mn

Room
Sala 5.5

 
     
 

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