Linear functional-differential equations on the line

G. Belitskii; V. Nicolaevsky

doi:10.1016/S0362-546X(97)00464-1

Linear functional-differential equations on the line

G. Belitskii, V. Nicolaevsky

Research output: Contribution to journal › Article › peer-review

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Abstract

Multidimensional equation ∑^l_j=1(D_jy)(F_jx) = γ(x) is considered. Here x ∈ ℝ¹ and D_J : C∞(ℝ¹, C ^m) → C∞(ℝ¹, C ⁿ) are given differential linear operators. We build a theory of this equation via "common dynamics" of maps F_j. In particular, it is proved that the operator T₀ : C∞(ℝ¹, C ^m) → C∞(ℝ¹, C ⁿ) with affine transformations F_jx = α_jx + β_j and differential linear operators Dj with constant coefficients is semi-Fredholm.

Original language	English
Pages (from-to)	2585-2593
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	30
Issue number	5
DOIs	https://doi.org/10.1016/S0362-546X(97)00464-1
State	Published - 1 Jan 1997

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "Linear functional-differential equations on the line",

abstract = "Multidimensional equation ∑lj=1(Djy)(Fjx) = γ(x) is considered. Here x ∈ ℝ1 and DJ : C∞(ℝ1, C m) → C∞(ℝ1, C n) are given differential linear operators. We build a theory of this equation via {"}common dynamics{"} of maps Fj. In particular, it is proved that the operator T0 : C∞(ℝ1, C m) → C∞(ℝ1, C n) with affine transformations Fjx = αjx + βj and differential linear operators Dj with constant coefficients is semi-Fredholm.",

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T1 - Linear functional-differential equations on the line

AU - Belitskii, G.

AU - Nicolaevsky, V.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Multidimensional equation ∑lj=1(Djy)(Fjx) = γ(x) is considered. Here x ∈ ℝ1 and DJ : C∞(ℝ1, C m) → C∞(ℝ1, C n) are given differential linear operators. We build a theory of this equation via "common dynamics" of maps Fj. In particular, it is proved that the operator T0 : C∞(ℝ1, C m) → C∞(ℝ1, C n) with affine transformations Fjx = αjx + βj and differential linear operators Dj with constant coefficients is semi-Fredholm.

AB - Multidimensional equation ∑lj=1(Djy)(Fjx) = γ(x) is considered. Here x ∈ ℝ1 and DJ : C∞(ℝ1, C m) → C∞(ℝ1, C n) are given differential linear operators. We build a theory of this equation via "common dynamics" of maps Fj. In particular, it is proved that the operator T0 : C∞(ℝ1, C m) → C∞(ℝ1, C n) with affine transformations Fjx = αjx + βj and differential linear operators Dj with constant coefficients is semi-Fredholm.

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U2 - 10.1016/S0362-546X(97)00464-1

DO - 10.1016/S0362-546X(97)00464-1

M3 - Article

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SN - 0362-546X

VL - 30

SP - 2585

EP - 2593

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 5

ER -

Linear functional-differential equations on the line

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