Entire bounded solutions for a class of sublinear elliptic equations Original Research Article

Let Ω be an arbitrary domain of View the MathML source and let ξ be a nonnegative locally bounded Borel function on Ω. In this paper, necessary and sufficient conditions are obtained for the existence of a nonnegative nontrivial bounded solution to the sublinear elliptic equation Δu=ξ(x)uγ in Ω where 0<γ⩽1. The special case of a radial function ξ is discussed in detail.