On the sign of the mountain pass solution Original Research Article

We consider a class of superlinear elliptic problems on a bounded domain Ω in Rn. It is known that (besides the zero solution) such superlinear problems 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 the effect of the nonlinearity on the sign of such ground-states and the corresponding role played by the “interior geometry” of Ω and the geometry of ∂Ω.