Large positive solutions to an elliptic system of competitive type with nonhomogeneous terms

In this paper, we study the elliptic system of competitive type with nonhomogeneous terms Delta u = upvq + h1(x), Delta v = urvs + h2(x) in omega with two types of boundary conditions: (I) u = v = +infinity and (SF) u = +infinity, v = f on partial differential omega, where f > 0, (p - 1)(s - 1) - qr > 0, and omega subset of RN is a smooth bounded domain. The nonhomogeneous terms h1(x) and h2(x) may be unbounded near the boundary and may change sign in omega. First, for a single semilinear elliptic equation with a singular weight and nonhomogeneous term, boundary asymptotic behaviour of large positive solutions is established. Using this asymptotic behaviour, we show existence of large positive solutions for this elliptic system with the boundary condition (SF), existence of maximal solution, boundary asymptotic behaviour and uniqueness of large positive solutions for this elliptic system with (I).