Asymptotic Behavior of Solutions of the Dirac System with an Integrable Potential
Keyword(s):
AbstractWe consider the Dirac system on the interval [0, 1] with a spectral parameter $$\mu \in {\mathbb {C}}$$ μ ∈ C and a complex-valued potential with entries from $$L_p[0,1]$$ L p [ 0 , 1 ] , where $$1\le p$$ 1 ≤ p . We study the asymptotic behavior of its solutions in a strip $$|\mathrm{Im}\,\mu |\le d$$ | Im μ | ≤ d for $$\mu \rightarrow \infty $$ μ → ∞ . These results allow us to obtain sharp asymptotic formulas for eigenvalues and eigenfunctions of Sturm–Liouville operators associated with the aforementioned Dirac system.
Keyword(s):
2012 ◽
Vol 36
(7)
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pp. 857-868
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Keyword(s):
2021 ◽
2020 ◽
Vol 11
(4)
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pp. 1805-1820