Existence of positive solutions for the Hénon equation involving critical Sobolev terms. (English) Zbl 1176.35083

Hirano, Norimichi

J. Differ. Equations 247, No. 5, 1311-1333 (2009).

Summary: Let \(N\geq 3\), \(2^*=2N/(N-2)\) and \(\Omega\subset\mathbb R^N\) be a bounded domain with a smooth boundary \(\partial\Omega\) and \(0\in\Omega\). Our purpose in this paper is to consider the existence of solutions of Hénon equation:
\[ -\Delta u(x)=|x|^\alpha |u(x)|^{2^*-1} \quad\text{in }\Omega, \qquad u>0\quad\text{in }\Omega, \qquad u=0\quad\text{on }\partial\Omega, \]
where \(\alpha>0\).

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
35J20	Variational methods for second-order elliptic equations
35B33	Critical exponents in context of PDEs

Keywords:

critical Sobolev terms; Hénon equation; semilinear elliptic problem

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