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

Alexandru Kristály, and Vicenţiu Rădulescu. "Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations." Studia Mathematica 191.3 (2009): 237-246. <http://eudml.org/doc/285008>.

@article{AlexandruKristály2009,
abstract = {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.},
author = {Alexandru Kristály, Vicenţiu Rădulescu},
journal = {Studia Mathematica},
keywords = {Emden–Fowler equation; sublinear eigenvalue problem; multiple solutions},
language = {eng},
number = {3},
pages = {237-246},
title = {Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations},
url = {http://eudml.org/doc/285008},
volume = {191},
year = {2009},
}

TY - JOUR
AU - Alexandru Kristály
AU - Vicenţiu Rădulescu
TI - Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations
JO - Studia Mathematica
PY - 2009
VL - 191
IS - 3
SP - 237
EP - 246
AB - 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.
LA - eng
KW - Emden–Fowler equation; sublinear eigenvalue problem; multiple solutions
UR - http://eudml.org/doc/285008
ER -