On the Hénon equation: asymptotic profile of ground states. I. (English) Zbl 1114.35071

Summary: This paper is concerned with the qualitative property of the ground state solutions for the Hénon equation. By studying a limiting equation on the upper half space \(\mathbb R_+^N\), we investigate the asymptotic energy and the asymptotic profile of the ground states for the Hénon equation. The limiting problem is related to a weighted Sobolev type inequality which we establish in this paper.


35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
47J30 Variational methods involving nonlinear operators
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