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

Alexandru Kristály; Vicenţiu Rădulescu — 2009

Studia Mathematica

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 $- Δ_{g} ω + α (σ) ω = K ̃ (λ, σ) f (ω)$ , 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...

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

Location of min-max critical points for multivalued functionals

A double eigenvalue problem for Schrödinger equations involving sublinear nonlinearities at infinity.

Critical point theorems on Finsler manifolds.