We prove the existence of a positive H01-solution for the equation-div(M(x) ▽u)=(f(x))/(up), 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.
TAN Yuxin
,
SUN Yijing
. Semilinear elliptic equations with strong singularity[J]. Journal of University of Chinese Academy of Sciences, 2017
, 34(6)
: 660
-666
.
DOI: 10.7523/j.issn.2095-6134.2017.06.002
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