Critical exponent for semilinear damped wave equations in the N-dimensional half space

We generalize a previous result of Ikehata (Math. Methods Appl. Sci., in press), which studies the critical exponent problem of a semilinear damped wave equation in the one-dimensional half space, to the general N-dimensional half space case. That is to say, one can show the small data global existence of solutions of a mixed problem for the equation u_tt−Δu+u_t=|u|^p with the power p satisfying p∗(N)=1+2/(N+1)<p?N/N−2]+ if we deal with the problem in the N-dimensional half space.