ACTA issues

On simultaneous approximations of continuous functions by solutions of an algebraic differential equation

C. Elsner

Acta Sci. Math. (Szeged) 67:3-4(2001), 697-708

Abstract. It is proved that finitely many continuous functions defined on the real line can be approximated simultaneously by $C^{\infty }({\msbm R}) $-solutions of the single algebraic differential equation $y_1'y_2''-y_2'y_1''=0 $ for any two of the approximating functions. Moreover, this result does no longer hold in the case of analytic solutions. A former result of the author is improved concerning the approximation of Lipschitz continuous functions by $C^{\infty }({\msbm R}) $-solutions of a third-order algebraic differential equation.

AMS Subject Classification (1991): 26A16, 26E10, 34A05

Received September 12, 2000. (Registered under 2811/2009.)