About some characteristics of average value of almost periodic square-law form

M. A. Voronetskaja

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2005), pp. 21-34

Résumé

Necessary and sufficient conditions of nonnegativity and necessary conditions of stronge positivity for average value of almost periodic in sense of Stepanov square-law form have been obtained. Those conditions have been used for obtaining of necessary second order conditions to solving of problem: $\lim\limits_{T\to\infty}\frac1T\int\limits_0^T L\bigl(t,x(t),\dot x(t)\bigr)\,dt\to\inf$, defined on the set of almost periodic functions in sense of Bohr, with the derivatives are almost periodic in sense of Stepanov.