On the stability of generalized hill''s equation with three independent parameters

This paper presents a stability criterion of a generalized Hill's equation with three independent parameters, examined by means of an asymptotic method. The theory has been applied to a special form of Hill's equation and the region of stability, has been graphically illustrated. The separatrix between bounded and unbounded solutions yields in parametric space the contour of a ‘stabilitatskörper’ in which the solution is always stable.