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

Byeon, Jaeyoung; Wang, Zhi-Qiang

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 23, No. 6, 803-828 (2006).

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.

MSC:

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

Keywords:

symmetry breaking; minimal energy solutions; asymptotic behaviour

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