Semilinear elliptic equations with strong singularity
Yuxin Tan, Sun Yijing · 2017
We prove the existence of a positive H01-solution for the equation-div(M(x) ▽u)= $\frac{{f\left( x \right)}}{{{u^p}}}$ , where M(x) is a bounded elliptic matrix (i. e., there exists 0 < α ≤ β such that M(x)ξ·ξ ≥ α|ξ|2, |M(x)|≤ β, ∀x ∈ Ω, ξ ∈ Rn), and -p < -1. The key to the work lies in establishing the validity and connection of two constraints which simplify the existence of a minimizer for the corresponding singular functional.