Arriagada, WaldoHuentutripay, Jorge2022-03-302022-03-302017-02-16Arriagada, W., & Huentutripay, J. (2017). Characterization of a homogeneous Orlicz space. <i>Electronic Journal of Differential Equations, 2017</i>(49), pp. 1-17.1072-6691https://hdl.handle.net/10877/15575In this article we define and characterize the homogeneous Orlicz space Do1,Φ(ℝN) where Φ : ℝ → [0, +∞) is the N-function generated by an odd, increasing and not-necessarily differentiable homeomorphism φ : ℝ → ℝ. The properties of Do1,Φ(ℝN) are treated in connection with the φ-Laplacian eigenvalue problem -div (φ(|∇u| ∇u/|∇u|) = λ g(⋅)φ(u) in ℝN where λ ∈ ℝ and g : ℝN → ℝ is measurable. We use a classic Lagrange rule to prove that solutions of the φ-Laplace operator exist and are non-negative.Text17 pages1 file (.pdf)enAttribution 4.0 Internationalhomogeneous spaceOrlicz spaceeigenvalue problemphi-LaplacianArticle