We investigate the singular solutions for the nonlinear elliptic equation \(-\Delta u =f(u)\) near the origin, and generalize the known multiplicity results for the model nonlinearity \(f(u)=u^p\) with \(\frac{N}{N-2}<p<\frac{N+2}{N-2}\) . Our analysis relies on the transformation introduced in Proposition 3.1 of [Fujishima-Ioku, J. Math. Pures Appl., 118 (2018), 128–158], which enables the reduction of equations with monotonically increasing nonlinearities to the corresponding prototypical power-type case. This approach yields multiplicity results for a broad class of nonlinearities, including \(f(s)=s^p+s^r\) with \(0<r<p\) , \(f(s)=s^p(\log s)^r\) with \(r\in \mathbb {R}\) , \(f(s)=s^p\exp ((\log s)^r)\) with \(0<r<1\) and \(f(s)=s^p+s^r(\log s)^{\beta }\) with \(0<r<p\) and \(\beta \in \mathbb {R}\) , for \(\frac{N}{N-2}<p<\frac{N+2}{N-2}\) .
