@Article{JPDE-8-341, author = {Chunlai Mu }, title = {Lp-Lq Estimates for a Linear Perturbed Klein-Gordon Equation}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {4}, pages = {341--350}, abstract = { We consider L^p-L^q estimates for the solution u(t,x) to tbe following perturbed Klein-Gordon equation ∂_{tt}u - Δu + u + V(x)u = 0 \qquad x∈ R^n, n ≥ 3 u(x,0) = 0, ∂_tu(x,0) = f(x) We assume that the potential V(x) and the initial data f(x) are compact, and V(x) is sufficiently small, then the solution u(t,x) of the above problem satisfies ||u(t)||_q ≤ Ct^{-a}||f||_p for t > 1 where a is the piecewise-linear function of 1/p and 1/q.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5666.html} }