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

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Kristály A., Rădulescu V.

Studia Mathematica

2009

tom 191

nr 3

237-246

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.

Ograniczanie wyników

1 Studia Mathematica

1 Kristály A.

1 Rădulescu V.

1 2009

Wyniki wyszukiwania

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