FRACTIONAL SPACES GENERATED BY THE SECOND ORDER DIFFERENTIAL OPERATOR WITH PERIODIC CONDITIONS
Proceedings of the Institute of Mathematics and Mechanics, vol.52, no.1, pp.25-47, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 52 Issue: 1
- Publication Date: 2026
- Doi Number: 10.30546/2409-4994.2026.52.1.02547
- Journal Name: Proceedings of the Institute of Mathematics and Mechanics
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.25-47
- Keywords: Boundary value problems, Green’s function, Periodic boundary conditions, Positivity of differential operators
- Open Archive Collection: AVESIS Open Access Collection
- Hacettepe University Affiliated: Yes
Abstract
In this study, we consider the second-order differential operator Ax defined by Axu = − (a(x)ux(x))x + σu(x), σ ⩾ 0, x ∈ R, with domain (Formula Presented) Estimates for the Green’s function are obtained. It is proved that for any α ∈ (0,1/2), the norms in the spaces Eα = Eα(˚C (ℝ), Ax) and ˚C2α (ℝ) are equivalent. The positivity of the operator Ax in Hölder spaces˚C2α (ℝ), α ∈ (0,1/2), is proved. As an application, theorems on well-posedness of local and nonlocal boundary value problems for elliptic equations in Hölder spaces are established.