Global bifurcation techniques for Yamabe type equations on Riemannian manifolds

We consider a closed Riemannian manifold (M-n, g) of dimension n >= 3 and study positive solutions of the equation -Delta(g)u + lambda u = lambda u(q), with lambda > 0, q > 1. If M supports a proper isoparametric function with focal varieties M-1, M-2 of dimension d(1) >= d(2) we show that for any q < n-d(2)+2/n-d(2)-2 the number of positive solutions of the equation -Delta(g)u+ lambda u = lambda u(q) tends to infinity as lambda -> +infinity. We apply this result to prove multiplicity results for positive solutions of critical and supercritical equations. We also obtain multiplicity results for the Yamabe equation on Riemannian manifolds. (C) 2020 Elsevier Ltd. All rights reserved.