Solutions with isolated point ruptures for a semilinear elliptic equation in R2 with a non-Lipschitz nonlinearity Original Research Article

We study the possible asymptotic behavior of u near an isolated rupture point for the following nonlinear equation with non-Lipschitz nonlinearity: Δu = uq, in B ⧹ {0}, u > 0, in B ⧹ {0}, where B = {x ϵ R2 : |x| < 1}, 0 < q < 1. Under some conditions, the asymptotic behavior of u at zero is characterized. As a result, we obtain the uniqueness of the solutions in R2 ⧹ {0}.