Perturbed nonlinear differential equations |
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Authors: | TG Proctor |
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Institution: | Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912 USA |
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Abstract: | The existence of a solution defined for all t and possessing a type of boundedness property is established for the perturbed nonlinear system y = f(t, y) + F(t, y). The unperturbed system x = f(t, x) has a dichotomy in which some solutions exists and are well-behaved as t increases to ∞ and some solution exists and are well-behaved as t decreases to ? ∞. A similar study is made for a perturbed nonlinear differential equation defined on a half line, say, R+, and the existence of a family of solutions with special boundedness properties is established. Finally, the ideas are applied to the study of integral manifolds. Examples are given. |
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