Periodic Solutions of a Non Linear Non Dissipative Wave Equation

P Rabinowitz

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P+Jl+... +Vl=n "T « ^ Jl+... +J^ Pt(x, t, u) - P^(x, t, UQ) =ZI ^mt"j •••^j m=l "i ''m y^ [ > P JL U . . . . U . -t- n-1 Ji+---+Jjji=" "^^ ^1 "^m It: n It n^ 2 P, u, . . . U . + Ft, (v +w ) j^^ nt^^n' n"0 ■ P. {x, t, u)-P. (:c, t, nQ)-F (x, t, UQ) • (u-Uq) .
Usinc our above estimate for v, we get Icoef. Or z'^ of F. (x, t, u) - P^(x, t, UQ)lQ l!"o'' ^^^ ^1 - HJ^u^^'^'^O^'' * ^^^ D = a{C-CQ) = a(A-AQ+ B^) (with Aq = Cq).
Suppose H(D) > 5c2p(D+aGQ)+ DP^(D+aCQ)(| + C, ^) + 1 and Q(D) >- G„(D) -^ ...+^ (1 + Zl) G(D) . Then v;e -et u [J a p j3^ v; ^s H(D) V -Vq ^Q(D) + gH(D)B .

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