Positive and multiple solutions of subcritical Emden-Fowler equations (Q1907737)

The author studies the semilinear elliptic equation \[ - \Delta u= f(x, u)\quad\text{in } \mathbb{R}^n,\;n\geq 3,\;u\in L^{2n/(n- 2)}(\mathbb{R}^n),\;\nabla u\in L^2(\mathbb{R}^n). \] Under several conditions on \(f\) the existence of a nontrivial solution is obtained. If in addition \(f\) is odd in the second variable, the existence of infinitely many solutions is proved.