Abstract
For density waves in a certain simplified model of a disk shaped galaxy, the dominant term of the basic equation (governing density waves) may be represented by a cubic polynomial, in which the stability parameter Q is allowed to be somewhat less than unity near corotation. For such a differential equation, an asymptotic form of the global dispersion relation is presented. It is shown that there exist discrete complex roots of the dispersion relation with small negative imaginary parts. The real parts and the imaginary parts of these roots represent approximately the angular speeds and the growth rate of the amplitudes of the density waves, respectively. It is proved that there exist only a finite number of unstable normal modes of density waves.
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