Positivity of the green functions for higher order ordinary differential equations

Michael I. Gil

Positivity of the green functions for higher order ordinary differential equations

Michael I. Gil

Department of Mathematics

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

2 Scopus citations

Abstract

We consider the equation ∑_k=0ⁿ _ak(t)x^(n-k)(t) = 0, t≥ 0, where a₀(t) ≡ 1, a_k(t) (k = 1,...,n) are real bounded functions. Assuming that all the roots of the polynomial zⁿ +a₁ (t)z ^n-1+ ⋯+a_n(t) (t ≥ 0) are real, we derive positivity conditions for the Green function for the Cauchy problem. We also establish a lower estimate for the Green function and a comparison theorem for solutions.

Original language	English
Pages (from-to)	1-7
Number of pages	7
Journal	Electronic Journal of Differential Equations
Volume	2008
State	Published - 25 Jul 2008

Keywords

Comparison of solutions
Fundamental solution
Green function
Linear ODE
Positivity

ASJC Scopus subject areas

Analysis

Cite this

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title = "Positivity of the green functions for higher order ordinary differential equations",

abstract = "We consider the equation ∑k=0n ak(t)x(n-k)(t) = 0, t≥ 0, where a0(t) ≡ 1, ak(t) (k = 1,...,n) are real bounded functions. Assuming that all the roots of the polynomial zn +a1 (t)z n-1+ ⋯+an(t) (t ≥ 0) are real, we derive positivity conditions for the Green function for the Cauchy problem. We also establish a lower estimate for the Green function and a comparison theorem for solutions.",

keywords = "Comparison of solutions, Fundamental solution, Green function, Linear ODE, Positivity",

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year = "2008",

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T1 - Positivity of the green functions for higher order ordinary differential equations

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N2 - We consider the equation ∑k=0n ak(t)x(n-k)(t) = 0, t≥ 0, where a0(t) ≡ 1, ak(t) (k = 1,...,n) are real bounded functions. Assuming that all the roots of the polynomial zn +a1 (t)z n-1+ ⋯+an(t) (t ≥ 0) are real, we derive positivity conditions for the Green function for the Cauchy problem. We also establish a lower estimate for the Green function and a comparison theorem for solutions.

AB - We consider the equation ∑k=0n ak(t)x(n-k)(t) = 0, t≥ 0, where a0(t) ≡ 1, ak(t) (k = 1,...,n) are real bounded functions. Assuming that all the roots of the polynomial zn +a1 (t)z n-1+ ⋯+an(t) (t ≥ 0) are real, we derive positivity conditions for the Green function for the Cauchy problem. We also establish a lower estimate for the Green function and a comparison theorem for solutions.

KW - Comparison of solutions

KW - Fundamental solution

KW - Green function

KW - Linear ODE

KW - Positivity

UR - http://www.scopus.com/inward/record.url?scp=48449103232&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:48449103232

SN - 1072-6691

VL - 2008

SP - 1

EP - 7

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Positivity of the green functions for higher order ordinary differential equations

Abstract

Keywords

ASJC Scopus subject areas

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