Eigenfunction and Green’s Function Asymptotics for Hill’s Equation with Symmetric Single-Well Potential

Kabataş A.

UKRAINIAN MATHEMATICAL JOURNAL, cilt.74, sa.2, ss.218-231, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 74 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s11253-022-02059-5
  • Dergi Adı: UKRAINIAN MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.218-231
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

We determine the asymptotic formulas for eigenfunctions of Hill's equation with symmetric single-well potential under periodic and semiperiodic boundary conditions. We apply the results for eigenvalues obtained by H. Coskun, et al. in (2019). By using these estimates for eigenfunctions, we obtain Green's functions related to Hill's equation. The method based on the work by C. T. Fulton (1977) is used to derive Green's functions in the asymptotic manner. We need the derivatives of the solutions in this method. Therefore, the asymptotic approximations for the derivatives of the eigenfunctions are also computed with different types of restrictions imposed on the potential.