Abstract
The goal of this paper is to discuss the continuous dependence of solutions on functional parameters for the following semilinear elliptic partial differential equation: Delta u(x) + (f) over bar (x, u(x), v(parallel to x parallel to)) + g(parallel to x parallel to)x . del u(x) = 0, for x is an element of Omega(r0) := {x is an element of R-n, n >= 3, parallel to x parallel to > r(0)} and v is an element of V, where V stands for some functional space. Our approach covers the case when f may change sign and admits general growth. As an additional result, the characterization of the radius r(0) for which our problem possesses at least one positive evanescent solution in the exterior domain Omega(r0) is described and numerically illustrated. Our approach relies on the subsolution and supersolution method and on a lemma due to Noussair and Swanson. (C) 2010 Elsevier Ltd. All rights reserved.