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Remarks on the Cauchy problem of Klein-Gordon equations with weighted nonlinear terms

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  • The Cauchy problem of Klein-Gordon equations is considered for power and exponential type nonlinear terms with singular weights. Time local and global solutions are shown to exist in the energy class. The Caffarelli-Kohn-Nirenberg inequality and the Trudinger-Moser type inequality with singular weights are applied to the problem.
    Mathematics Subject Classification: Primary: 35L70; Secondary: 35L15.


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