Generalized Yamabe equations on Riemannian manifolds and applications to Emden-Fowler problems

Abstract

In this paper, we establish the existence of solutions and multiplicity properties for generalized Yamabe equations on Riemannian manifolds.  Problems of this type arise in conformal Riemannian geometry, astrophysics, and in the theories of thermionic emission, isothermal stationary gas sphere, and gas combustion. The abstract results of this paper are illustrated with Emden-Fowler equations involving sublinear terms at innity. Two examples reveal the analytic setting of this paper.

Key words: Three solutions, generalized Yamabe equations, Riemannian manifold, Emden-Fowler problem, variational methods.