Abstract: We investigate the strongly singular partial differential equations of matrix-type,

where Ω is a bound and open set in Rⁿ, M(x) is a real symmetric matrix on Ω, -p<-1,0 < q < 1,λ>0 are parameters, f(x)∈L¹(Ω),f(x)>0 a.e. in Ω. We prove that the above-mentioned equation admits at least one positive H₀¹-solution when λ>0 if there exists u₀ ∈H₀¹(Ω) such that ∫_Ωf(x)|u₀|^1-pdx <+∞. It should be noted that a classical solution, namely, the C²(Ω)∩C(Ω)-solution, is not necessarily a H₀¹(Ω)-solution for singular equations.

Key words: H₀¹-solution, real symmetric matrix, strong singularity