
Existence results for the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
Keywords: 35J60; 53C21; 53C80; 58E05; 58J45; 83C05Einstein-scalar field equation; Lichnerowicz equation; Picone type identity; Critical exponent; Negative exponent; Mountain pass theorem; Palais–Smale condition; Sign-changing nonlinearity