We shall introduce, in this chapter, several possible areas of investigation of dynamic systems on time scales that await further progress. In Section 4.1, we shall develop the methods of upper and lower solutions and monotone iterative technique for initial and periodic boundary value problems. Section 4.2 is devoted to the method of generalized quasilinearization which offers not only monotone sequences that converge to the unique solution but also shows that the convergence is quadratic.
KeywordsRiccati Equation Invariant Manifold Invariance Principle Nonoscillatory Solution Monotone Sequence
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