Minimal periods for solutions of semilinear wave equations in exterior domains and for solutions of the equations of nonlinear elasticity

AbstractLet g ϵ C2(R1) and u(r, t) solve urr + ((n − 1)r) ur − utt − g(u) = 0 classically on D0 = (0, ∞) × [0, T] and be periodic in time. If limr → + ∞r2(n − 1)E(r) = limr → ∞ ∥u(r,·)∥∞ = 0, where E(r) = ∫0T (ur2 + ut2) dt, u ϵ L1(Dr1) for some r1 > 0, and g′(0) > (2πT)2, then u is independent of T. Related results are obtained for the equations of nonlinear elasticity