DECAY PROPERTIES OF PERIODIC, RADIALLY SYMMETRICAL SOLUTIONS OF SINE-GORDON-TYPE EQUATIONS

We investigate the radially symmetric, nonlinear wave equation u(u) = r(-n)(r(n)u(r))r - lambdau - F(u), n greater-than-or-equal-to 2 and discuss the asymptotic behaviour as r --> infinity of solutions which are T-periodic in time t. It is shown that only two possibilities of decay can arise, namely polynomial like t-1/2(n-1) and exponential e(-bt) for some b > 0. Existence results are obtained.