We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds (B,g_B) and (F,g_F) furnished with metrics of the form c^2g_B ⊕ w^2 g_F and, in particular, of the type w^2 μg_B ⊕ w^2 g_F, where c, w B → (0,∞) are smooth functions and μ is a real parameter. We obtain suitable expressions for the Ricci tensor and scalar curvature of such products that allow us to establish results about the existence of Einstein or constant scalar curvature structures in these

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... s. If (B,g_B) is Riemannian, the latter question involves nonlinear elliptic partial differential equations with concave-convex nonlinearities and singular partial differential equations of the Lichnerowicz-York type among others.