On the Hénon equation: asymptotic profile of ground states. II. (English) Zbl 1114.35070

Byeon, Jaeyoung; Wang, Zhi-Qiang

J. Differ. Equations 216, No. 1, 78-108 (2005).

Summary: This paper is concerned with analyzing the limiting behavior of the least energy solutions for the Hénon equation
\[ -\Delta u=| x|^\alpha u^{p-1},\quad u>0 \text{ in }\Omega, \quad u=0 \text{ on } \partial\Omega \] where \(\Omega\) is a bounded domain in \(\mathbb R^N\) with \(N\geq 3\), \(2<p<2^*\cong {2N\over N-2}\). We study the problems in bounded domains with smooth or non-smooth boundaries, and in particular we examine the effect of the boundary on the limiting profile of the solutions.
Part I, cf. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 23, No. 6, 803–828 (2006; Zbl 1114.35071).

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:

Least energy solutions; Hénon equation; Limiting profile; Weighted equations

Citations:

Zbl 1114.35071

References:

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