Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations

Let (M, g) be a compact Riemannian manifold without boundary, with dim M >= 3, and f : R -> R a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem -Delta(g)w + alpha(sigma)w = (K) over tilde(lambda, sigma)f(w), sigma is an element of M, w is an element of H(1)(2)(M), is established for certain eigenvalues lambda > 0, depending on further properties of f and on explicit forms of the function (K) over tilde. Here, Delta(g) stands for the Laplace-Beltrami operator on (M, g), and alpha, (K) over tilde are smooth positive functions. These multiplicity results are then applied to solve Emden-Fowler equations which involve sublinear terms at infinity.