We study the existence of positive solutions to classes of $n\times n$ systems of reaction diffusion equations with Dirichlet boundary conditions. In particular, we consider systems where the reaction terms approach $-\infty$ near the origin and satisfy a combined sublinear condition at $\infty .$ We use the method of sub-super solutions to establish our results.
Eun Kyoung Lee. R. Shivaji. Jinglong Ye. "Classes of infinite semipositone $n \times n$ systems." Differential Integral Equations 24 (3/4) 361 - 370, March/April 2011. https://doi.org/10.57262/die/1356019036