Abstract

We consider radial solutions of a general elliptic equation involving a weighted Laplace operator. We establish the uniqueness of the radial bound state solutions to div(A del v) + Bf(v) = 0, lim(vertical bar x vertical bar ->+infinity) v(x) 0, x is an element of R-n, (P) n > 2, where A and B are two positive, radial, smooth functions defined on R-n {0}. We assume that the nonlinearity f is an element of C(-c, c), 0 < c <= infinity is an odd function satisfying some convexity and growth conditions, and has a zero at b > 0, is non positive and not identically 0 in (0, b), positive in (b, c), and is differentiable in (0, c).