This paper investigates the multiplicity of singular solutions for the nonlinear elliptic equation $-\Delta u =f(u)$ near the origin. Applying the classification of nonlinear functions and the transformation, which were developed by the authors, we generalize the multiplicity results known for the concrete model nonlinearity $f(u)=u^p$ with $\frac{ N}{ N-2}<p<\frac{ N+2}{ N-2}$. Our result applies to various nonlinearities, such as $f(s)=s^p+s^r$ 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 $\frac{ N}{ N-2}<p<\frac{ N+2}{ N-2}$.
Categories: math.AP