We study the competition model Λut (x, t) -d 1 (x) Du(x, t)
where the coefficient functions are strictly positive over the underlying spatial region W except b(x), which vanishes in a nontrivial subdomain of W, and is positive in the rest of W. We show that there exists a critical number l g such that if l < l g , then the model behaves similarly to the well-studied classical competition model where all the coefficient functions are positive constants, but when l > l g , new phenomena occur. Our results demonstrate the fact that heterogeneous environmental effects on population models are not only quantitative, but can be qualitative as well. In part I here, we mainly study two kinds of steady-state solutions which determine the dynamics of the model: one consists of finite functions while the other consists of generalized functions which satisfy (u, v)=(., 0) on the part of the domain that b(x) vanishes, but are positive and finite on the rest of the domain, and are determined by certain boundary blow-up systems. The research is continued in part II, where these two kinds of steady-state solutions will be used to determine the dynamics of the model.