A generic multiplicity result for a Yamabe-type equation via Morse theory - Ramos, Gustavo de Paula (2020)
Let M^n be a closed manifold with n>=3 and (N, h) be a Riemannian manifold with positive constant scalar curvature. We prove that a PDE similar to the Yamabe equation on the Riemannian product (MxN,g+h\\epsilon^2) depending only on conformal factors u\\colon M \\to \\mathbb has at least P_1(M) positive solutions with small energy for generic (\\epsilon,g), where \\epsilon>0 is sufficiently small and g is a Riemannian metric of class C^k on M, 2<=k<\\infty. This result is obtained by adapting techniques employed by Micheletti & Pistoia (2009), Ghimenti & Micheletti (2011) and Jimmy Petean (2016).