Positive mountain pass solutions for a semilinear elliptic equation with a sign-changing weight function

We use the mountain pass theorem to study the existence and multiplicity of positive solutions of the generalisation of the well-known logistic equation -Δu=λg(x)u(x)(1-u(x))-Δu=λg(x)u(x)(1-u(x)) with Dirichlet boundary conditions to the case where g changes sign.