Positivity of the green functions for higher order ordinary differential equations

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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.

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalElectronic Journal of Differential Equations
Volume2008
StatePublished - 25 Jul 2008

Keywords

  • Comparison of solutions
  • Fundamental solution
  • Green function
  • Linear ODE
  • Positivity

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