On the sign of the mountain pass solution

We consider a class of superlinear elliptic problems on a bounded domain Om ega in R-n. It is known that (besides the zero solution) such superlinear p roblems possess at least one positive and one negative solution of mountain -pass type, as well as a sign-changing solution. Moreover, the least-energy solutions ("ground-states") are among those one-sign solutions. We study t he effect of the nonlinearity on the sign of such ground-states and the cor responding role played by the "interior geometry" of Omega and the geometry of partial derivative Omega. (C) 2001 Elsevier Science Ltd. All rights res erved.