Abstract
This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations Delta u(x) + f(x, u(x)) + g(parallel to x parallel to)x . del u(x) = 0, x is an element of R-n, parallel to x parallel to > R. We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy f(x, 0) equivalent to 0. The asymptotic behavior of solutions is also described. (C) 2008 Elsevier Inc. All rights reserved.