In a domain specified in the form of a Cartesian product of a segment [0, T] and the space \( {{\mathbb{R}}^p} \), we study a problem with integral conditions with respect to the time variable for Gårding hyperbolic equations with constant coefficients in the class of functions almost periodic in the space variables. A criterion for the unique solvability of this problem and sufficient conditions for the existence of its solution are established in different function spaces. To solve the problem of small denominators arising in the construction of solutions of the posed problem, we use the metric approach.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 2, pp. 252–265, February, 2013.
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Kuz’, A.M., Ptashnyk, B.I. A problem with integral conditions with respect to time for Gårding hyperbolic equations. Ukr Math J 65, 277–293 (2013). https://doi.org/10.1007/s11253-013-0777-7
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DOI: https://doi.org/10.1007/s11253-013-0777-7