Abstract:
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.
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