Principal solutions of non-oscillatory half-linear differential equations. (English) Zbl 0914.34031

Elbert, Árpád; Kusano, Takaŝi

Adv. Math. Sci. Appl. 8, No. 2, 745-759 (1998).

Summary: The notion of the principal solution to nonoscillatory linear differential equations of second order is generalized to nonoscillatory half-linear second-order differential equations. Relations are established between the principal solutions to two differential equations when one of the differential equations is a Sturmian majorant of the other one. An application is given to the Bessel function \(K_0(t)\).

MSC:

34C10

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

Keywords:

principal solution; nonoscillatory half-linear second-order differential equations; Sturmian majorant; Bessel function