Existence and asymptotic behavior of non-radially symmetric ground states of semilinear singular elliptic equations

This paper deals with the existence and asymptotic behavior of entire positive solutions of the semilinear elliptic equation −Δu=ρ(x)f(u)inRN(N≥3), where ρρ is nonnegative and locally Hölder continuous and ff is a positive locally Lipschitz continuous function, singular at 0 in the sense that f(r)⟶r→0∞. No symmetry is required from ρρ and no monotonicity condition is imposed on ff. Arguments for lower and upper solutions are exploited.