Abstract
The aim of this paper is to prove some energy estimates for Klein–Gordon equations with time-dependent potential. If the potential is “non-effective” and has “very slow oscillations” in the time-dependent coefficient, then energy estimates are proved in Ebert et al. (in: Dubatovskaya and Rogosin (eds) AMADE 2012, Cambridge Scientific Publishers, Cambridge, 2014). In contrast, the main goal of the present paper is to generalize the previous results to potentials with “very fast oscillations” in the time-dependent coefficient; consequently, the positivity of the potential is not required anymore.
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