On transformations of two homogeneous linear second order differential equations of a general and of Sturm forms. (English) Zbl 0643.34048

Laitochová, Jitka

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 85, Math. 25, 77-95 (1986).

Let (ab): \(y''+a(t)y'+b(t)=0\), \(a,b\in C^ 0(j)\), (AB): \(Y''+A(T)Y'+B(T)Y=0\), \(A,B\in C^ 0(J)\) be two second order homogeneous linear differential equations. Necessary and sufficient conditions for two functions \(f=f(t)\), \(h=h(t)\), \(t\in j\), so that every solution Y of (AB) the function \(y(t)=f(t)\cdot Y[h(t)]\) is a solution of (a,b) in \(i\subset j\) are given. These conditions are also formulated for equations of Sturm and Jacobi type.

Reviewer: J.Laitochová

MSC:

34C20	Transformation and reduction of ordinary differential equations and systems, normal forms
34A30	Linear ordinary differential equations and systems

Keywords:

Jacobi equation; Sturm equation; second order homogeneous linear differential equations

References:

[1]	Borůvka O.: Linear Differential Transformations of the Second Order. The English University Press, London, 1971. · Zbl 0218.34005
[2]	Neuman F.: Teorija globalnych svojstv obyknovennych linějnych differencialnych uravnenij n-go porjadka. Differencialnye uravnenija 19 (1983), 799-808.