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

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).


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


Zbl 1114.35071
Full Text: DOI


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