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<p/> <p>We analytically establish the conditions for the existence of at least two or three positive solutions in the generalized <inline-formula><graphic file="1687-1847-2009-848191-i2.gif"/></inline-formula>-point boundary value problem for the <inline-formula><graphic file="1687-1847-2009-848191-i3.gif"/></inline-formula>-Laplacian dynamic equations on time scales by means of the Avery-Henderson fixed point theorem and the five functionals fixed point theorem. Furthermore, we illustrate the possible application of our analytical results with a concrete and nontrivial dynamic equation on specific time scales.</p>