Sublinear eigenvalue problems on compact Riemannian manifolds with applications in emden-fowler equations

Alexandru Kristály, Vicenţiu Rǎdulescu

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9 Citations (Scopus)

Abstract

Let (M,g) be a compact Riemannian manifold without boundary, with dim M ≤ 3, and π : ℝ → ℝ a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem -Δgω + α(σ)ω = K̄(λ, σ)π(ω), σ ∈ M, ω ∈ H21(M), is established for certain eigenvalues λ > 0, depending on further properties of π and on explicit forms of the function K̄. Here, Δg stands for the Laplace-Beltrami operator on (M, g), and α, K̄ are smooth positive functions. These multiplicity results are then applied to solve Emden-Fowler equations which involve sublinear terms at infinity.

Original languageEnglish
Pages (from-to)237-246
Number of pages10
JournalStudia Mathematica
Volume191
Issue number3
DOIs
Publication statusPublished - Jul 13 2009

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Keywords

  • Emden-Fowler equation
  • Multiple solutions
  • Sublinear eigenvalue problem

ASJC Scopus subject areas

  • Mathematics(all)

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