Compatibility conditions for the existence of weak solutions to a singular elliptic equation.

This paper deals with the existence of positive solutions to the singular elliptic boundary value problem involving p-Laplace operator ... where Ω⊂ RN (N = 1) is a bounded domain with smooth boundary ∂ Ω, h ∈ L¹(Ω), h(x) > 0 almost everywhere in Ω, k ∈ L∞(Ω) is nonnegative, p > 2, α > 1 and ß ∈ (0, p - 1). A compatibility condition on the couple (h(x),a) is given for the problem to have at least one solution. More precisely, it is shown that the problem admits a solution if and only if there exists u0 ∈ H¹0(Ω) such that ƒΩ hu01-a 0 dx <∞. [ABSTRACT FROM AUTHOR]