The spectral problem
\[-y''+q(x)y=\lambda y,\ \ \ \ 0<x<1\]
\[y(0)=0, \quad y'(0)=\lambda(ay(1)+by'(1)),\]
is considered, where $\lambda$ is a spectral parameter, $q(x)\in{{L}_{1}}(0,1)$ is a complex-valued function, $a$ and $b$ are arbitrary complex numbers which satisfy the condition $|a|+|b|\ne 0$. We study the spectral properties (existence of eigenvalues, asymptotic formulae for eigenvalues and eigenfunctions, minimality and basicity of the system of eigenfunctions in ${{L}_{p}}(0,1)$) of the above-mentioned Sturm-Liouville problem.
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 6 Ağustos 2020 |
Yayımlandığı Sayı | Yıl 2020 Cilt: 49 Sayı: 4 |