Disconjugacy characterization by means of spectral of (k,n-k) problems

2015/06/09 by Alberto Cabada, Cabada, Alberto, Lorena Saavedra +1
Mathematics · #34B07 #34B08 #34B27 #34C10 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1506.03043

openalex publication_date 2015/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the description of the interval of parameters for which the general linear n^{\rm th}-order equation T_n[M] u(t) ≡ u⁽ⁿ⁾(t)+a₁(t) u^(n-1)(t)+⋯ +a_n-1(t) u'(t)+(a_n(t)+M) u(t)=0 , t∈ I≡[a,b], with a_i∈ C^n-i(I), is disconjugate on I . Such interval is characterized by the closed to zero eigenvalues of this problem coupled with (k,n-k) boundary conditions, given by u(a)=⋯=u^(k-1)(a)=u(b)=⋯=u^(n-k-1)(b)=0 , 1≤ k≤ n-1 .

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