Multiple solutions of generalized Yamabe equations on Riemannian manifolds and applications to Emden–Fowler problems

The existence of three nontrivial solutions for a nonlinear problem on compact dd-dimensional (d≥3d≥3) Riemannian manifolds without boundary, is established. This multiplicity result is then applied to solve Emden–Fowler equations that involve sublinear terms at infinity. Two concrete examples are also provided in the present paper. Our results apply to problems arising in conformal Riemannian geometry, astrophysics, and in the theories of thermionic emission, isothermal stationary gas sphere, and gas combustion.