09-191 F. Genoud

A uniqueness result for $\Delta u -\lambda u + V(\vert x\vert)u\sp p=0$ on $\mathbb{R}\sp 2$ (230K, pdf) Oct 20, 09

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Abstract. Uniqueness of positive radial solutions decaying at infinity is proved for a class of semilinear elliptic equations on $\mathbb{R}\sp 2$. Complementary results for the same kind of equations were obtained in the early 90's, on $\mathbb{R}\sp N$ with $N\geq3$, and in finite balls of $\mathbb{R}\sp N$ with $N\geq2$. The new result presented here plays a crucial role in the global bifurcation problem, previously studied by the author.

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