Spectral properties of fourth order differential operators. (English) Zbl 0894.34028

Došlý, O.; Hilscher, R.

Math. Bohem. 122, No. 2, 153-168 (1997).

Summary: Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of singular differential operators \(\ell (y) \equiv \frac 1{w(t)} (r(t)y'')''\), \(t\in [a,\infty)\) are established. These conditions are based on a recently proved relationship between spectral properties of \(\ell \) and oscillation of a certain associated second-order differential equation.

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

singular differential operators; property BD; oscillation criteria; principal solution