Initial value parameters corresponding to positive Green’s functions. (English) Zbl 0759.34028

Kreith, Kurt

Arch. Math., Brno 27b, 161-166 (1991).

The author establishes criteria for the positivity of the Green’s function associated with the real fourth order linear equation (*) \((P_ 2(t)v''-Q_ 2(t)v')''-(P_ 1(t)v'-Q_ 1(t)v)'+P_ 0(t)v=0\) and the conjugate point boundary condition (**) \(v(0)=v'(0)=0=v(\eta)=v'(\eta)\) where \(\eta\in(0,\eta_ 1)\) and \(\eta_ 1\) is the smallest \(t>0\) for which (**) is realized by a nontrivial solution of (*).

Reviewer: J.Diblík (Brno)

MSC:

34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34B05	Linear boundary value problems for ordinary differential equations
34B27	Green’s functions for ordinary differential equations

Keywords:

positivity; Green’s function; real fourth order linear equation; conjugate point boundary condition