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

Alexandru Kristály ; Vicenţiu Rădulescu

Studia Mathematica, Tome 192 (2009), p. 237-246 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $-Δ_{g}ω + α(σ)ω = K̃(λ,σ)f(ω)$, σ ∈ M, ω ∈ H₁²(M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, $Δ_{g}$ 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.

Détail

Publié le : 2009-01-01

Zbl 1213.58022

EUDML-ID : urn:eudml:doc:285008