Wachstumsordnung und Index der Lösungen linearer Differentialgleichungen mit rationalen Koeffizienten.
The existence of a traveling wave with special properties to modified KdV and BKdV equations is proved. Nonlinear terms in the equations are defined by means of a function f of an unknown u satisfying some conditions.
Picone identity for a class of nonlinear differential equations is established and various qualitative results (such as Wirtinger-type inequality and the existence of zeros of first components of solutions) are obtained with the help of this new formula.