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Vector spaces over function fields. Vector spaces over analytic function fields being associated to ordinary differential equations. (English) Zbl 0966.47028

Summary: It is a well-known fact, that the general solution of a linear ordinary differential equation belongs to a function vector space over the real (complex) number field generated by a finite exponential function set. This circumstance allows us to handle the large-time behavior and stability problems easily. However there is a wide class of nonlinear differential equations whose solutions belong to some function space being also generated by an arbitrary exponential function set; so that the stability problems can be handled as in the linear case. To discern whether a given autonomous system belongs to such an equation class, sufficient conditions have been stated in a previous article. Now, we generalize those conditions to a wider class of nonlinear autonomous systems.

MSC:

47E05 General theory of ordinary differential operators
46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.)
46N20 Applications of functional analysis to differential and integral equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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