On the location of zeroes of oscillatory solutions of \(y^{(n)}=c(x)y\)
It is known that the location of zeroes of solutions of differential equations is important to the study of certain boundary value problems and to certain eigenvalue problems. The location of zeroes of solutions of wide classes of differential equations \(y^{(n)}=c(x)y\) is obtained on an infinite interval. The structure of the subspaces of oscillatory solutions is given in detail. This leads to oscillation and nonoscillation criteria. Prufer type representations are produced for this high order differential equation. Asymptotic techniques are used. The finer asymptotic behaviour of solutions and their derivatives up to the n-th order is revealed. The usefulness of the definition ''almost diagonal systems'' is demonstrated.
scientific article; zbMATH DE number 3882765
scientific article