Existence, uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations

We study positive solutions of the Dirichlet problem: Δ u ( x )+ f ( u ( x ))=0, x ∈ D n , u ( x )=0, x ∈∂ D n , where D n is an n -ball. We find necessary and sufficient conditions for solutions to be nondegenerate. We also give some new existence and uniqueness theorems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46528/1/220_2005_Article_BF01468138.pd