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

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
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