Supersolutions to degenerated logistic equation type

In this work we provide a method for building up a strictly positive supersolution for the steady state of a degenerated logistic equation type, i.e., when the weight function vanishes on the boundary of the domain. This degenerated system is related in obtaining the so-called large solutions. Previously, this problem was handled as the limit case of non degenerated approaching problems. Our method can be adapted straightforwardly to degenerated boundary value problems.