A variational approach to a class of singular semilinear elliptic equations. (English) Zbl 1073.35092

Canino, Annamaria; Degiovanni, Marco

J. Convex Anal. 11, No. 1, 147-162 (2004).

The authors deal with singular semilinear elliptic problems of the form \[ -\Delta u= u^{-\beta}+ g(x,u)\quad \text{in }\Omega,\qquad u> 0\quad \text{in }\Omega,\qquad u= 0\quad \text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is a bounded open subset of \(\mathbb{R}^n\), \(\beta> 0\), and \(g\) satisfies suitable growth conditions. The main goal of the authors is to provide a variational approach to (1).

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
49J40	Variational inequalities
35J20	Variational methods for second-order elliptic equations
35J25	Boundary value problems for second-order elliptic equations
47J30	Variational methods involving nonlinear operators

Keywords:

semilinear elliptic problems; variational approach