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

Let (M, g) be a compact Riemannian manifold without boundary, with dimM ≥ 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 −∆gω + α(σ)ω = K̃(λ, σ)f(ω), σ ∈M, ω ∈ H 1 (M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, ∆g stands for the Laplace–Beltrami operator on (M, g), and α, K̃ are smooth positive functions. These multiplicity results are then applied to solve Emden–Fowler equations which involve sublinear terms at infinity.