@MISC{_analmost-periodicity, author = {}, title = {AN ALMOST-PERIODICITY CRITERION FOR SOLUTIONS OF THE OSCILLATORY DIFFERENTIAL EQUATION y00 = q(t)y AND ITS APPLICATIONS}, year = {} }

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Abstract

Abstract. The linear dierential equation (q) : y00 = q(t)y with the uni-formly almost-periodic function q is considered. Necessary and sucient conditions which guarantee that all bounded (on R) solutions of (q) are uni-formly almost-periodic functions are presented. The conditions are stated by a phase of (q). Next, a class of equations of the type (q) whose all non-trivial solutions are bounded and not uniformly almost-periodic is given. Finally, uniformly almost-periodic solutions of the non-homogeneous dierential equa-tions y00 = q(t)y + f(t) are considered. The results are applied to the Appell and Kummer dierential equations. 1.