We consider Dirichlet problems of the form -/x/(alpha) Deltau = lambdau + g
(u) in Omega, u = 0 on partial derivative Omega, where alpha, lambda is an
element of R, g is an element of C(R) is a superlinear and subcritical func
tion, and Omega is a domain in R-2. We study the existence of positive solu
tions with respect to the values of the parameters alpha and X, and accordi
ng that 0 is an element of Omega or 0 is an element of partial derivative O
mega, and that Omega is an exterior domain or not.