BREZIS-KAMIN TYPE RESULTS INVOLVING LOCALLY INTEGRABLE WEIGHTS

We study existence and asymptotic behavior of entire posi-tive bounded solutions for the following class of semilinear elliptic problem{L(u) = & rhov;(x)f (x, u) in R-N, N >= 3,u > 0, in R-N,where 0 <= & rhov; is an element of L-loc(p)(R-N), for some N < p <= oo. Here, L is a local uniform elliptic operator and f(x, s) is a nonlinearity with sublinear behavior at zero and at +infinity. This type of result has already been studied in the celebrated work by H. Brezis and S. Kamin for the case when L = -triangle and & rhov; E L-loc(infinity)(R-N). Our approach allows us to include for instance -div ((1 + |x|(mu))(nu)triangle u) = u(q)(|x|(alpha) + |x|(beta))-1 with suitable alpha, beta > 0, mu, nu E R and 0 < q < 1. Here, we include two local uniform elliptic situations: mu > 0 with nu = 1 or nu = -1.