Positive Solutions of an Indefinite Prescribed Mean Curvature Problem on a General Domain

The existence of positive solutions is proved for the prescribed mean curvature problem where Ω ⊂ℝ is a bounded smooth domain, not necessarily radially symmetric. We assume that ∫ f(x, s) ds is locally subquadratic at 0, ∫ g(x, s) ds is superquadratic at 0 and λ > 0 is sufficiently small. A multiplicity result is also obtained, when ∫ f(x, s) ds has an oscillatory behaviour near 0. We allow f and g to change sign in any neighbourhood of 0.