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.
📌 3 Key Takeaways
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Objective & Hypothesis: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 $|a|+|b|\ne 0$.
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Key Findings & Data: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 $|a|+|b|\ne 0$.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:eigenvalues · eigenfunctions · minimal system
Abstract
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.
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