Abstract
We consider the Cauchy problem for the semilinear wave equation \({u_{tt} - \Delta u + V(x)u_t = |u|^p}\) .When \({V(x) = V_0(1 + |x|^2)^{-1/2}, V_0 \geq n}\) , we prove that the critical exponent for the problem is \({p_c(n)=\left\{\begin{array}{ll} 1+\frac{2}{n-1},& n \geq 2,\\ +\infty,& n=1. \end{array}\right.}\)
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Li, X. Critical exponent for semilinear wave equation with critical potential. Nonlinear Differ. Equ. Appl. 20, 1379–1391 (2013). https://doi.org/10.1007/s00030-012-0214-x
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DOI: https://doi.org/10.1007/s00030-012-0214-x