Asymptotics of the Fundamental System Solutions of Differential Equation With Block-Triangular Operator Potential

Kholkin, Aleksandr M

doi:10.17654/ms102102359

Cited by 1 publication

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“…Use (12) to differentiate (27), then find the asymptotes of Ψ0 x, λ ðÞ as x ! ∞ similarly to (21) to obtain the second part of formula (13). Theorem is proved.…”

Section: Construction Of the Fundamental System Of Solutions For An Operator Differential Equation With A Rapidly Increasing At Infinity mentioning

confidence: 79%

“…The solution Ψ x, λ ðÞ given by Ψ x, λ (13). Use (12) to differentiate (27), then find the asymptotes of Ψ0 x, λ ðÞ as x !…”

Section: Construction Of the Fundamental System Of Solutions For An Operator Differential Equation With A Rapidly Increasing At Infinity mentioning

confidence: 99%

“…In the context of the inverse scattering problem, for an operator with a triangular matrix potential decreasing at infinity, the first moment of which is bounded, the structure of the spectrum was established in [9,10]. The theory of equations with block -triangular operator coefficients the first results were published in 2012 in the works of the author [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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Spectral Properties of a Non-Self-Adjoint Differential Operator with Block-Triangular Operator Coefficients

Kholkin¹

2021

Recent Developments in the Solution of Nonlinear Differential Equations

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In this chapter, the Sturm-Liouville equation with block-triangular, increasing at infinity operator potential is considered. A fundamental system of solutions is constructed, one of which decreases at infinity, and the second increases. The asymptotic behavior at infinity was found out. The Green’s function and the resolvent for a non-self-adjoint differential operator are constructed. This allows to obtain sufficient conditions under which the spectrum of this non-self-adjoint differential operator is real and discrete. For a non-self-adjoint Sturm-Liouville operator with a triangular matrix potential growing at infinity, an example of operator having spectral singularities is constructed.

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“…Use (12) to differentiate (27), then find the asymptotes of Ψ0 x, λ ðÞ as x ! ∞ similarly to (21) to obtain the second part of formula (13). Theorem is proved.…”

Section: Construction Of the Fundamental System Of Solutions For An Operator Differential Equation With A Rapidly Increasing At Infinity mentioning

confidence: 79%

“…The solution Ψ x, λ ðÞ given by Ψ x, λ (13). Use (12) to differentiate (27), then find the asymptotes of Ψ0 x, λ ðÞ as x !…”

Section: Construction Of the Fundamental System Of Solutions For An Operator Differential Equation With A Rapidly Increasing At Infinity mentioning

confidence: 99%