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

• Autorzy: Alexandru Kristály , Vicenţiu Rădulescu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 58J05: Elliptic equations on manifolds, general theory
• 35J60: Nonlinear elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 191
• Numer: 3
• Strony: 237-246

Daty

wydano

2009

Twórcy

autor

Alexandru Kristály

• Department of Economics, University of Babeş-Bolyai, 400591 Cluj-Napoca, Romania

autor

Vicenţiu Rădulescu

• Institute of Mathematics "Simion Stoilow", of the Romanian Academy, 014700 Bucureşti, Romania
• Department of Mathematics, University of Craiova, 200585 Craiova, Romania

Identyfikatory

DOI

10.4064/sm191-3-5