Singular solutions for semilinear elliptic equations with general supercritical growth

Abstract A positive radial singular solution for $$\Delta u+f(u)=0$$ Δ u + f ( ) = 0 with a general supercritical growth is constructed. An exact asymptotic expansion as well its uniqueness in the space of functions are also established. These results can be applied to bifurcation problem u+\lambda f(u)=0$$ λ on ball. Our method treat wide class nonlinearities unified way, e.g., $$u^p\log u$$ p log , $$\exp (u^p)$$ exp and (\cdots \exp (u)\cdots )$$ ⋯ $$u^p$$ $$e^u$$ e . Main technical tools intrinsic transformations semilinear elliptic equations ODE techniques.