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Additional info for A note on the existence of H-bubbles via perturbation methods

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29 we have G pn with a constant C3 > 0 depending only on GQ. 9. rl'Nu2ds. 8. 42. The function A is called Dini continuous at zero if DEFINITION the integral 0 is finite for some d > 0. 43. 1) 0

Then h oo B(h) = J^dt=Z 2~kh I oo ^ lnn^4(tn) > - lnnA(ntn), tn and Bint ) 1 lim ntn — 0. A(ntn) e n->oo Thus A(t) and B(t) are not equivalent. 6) sup ^Q

Ti o ^11(70,^(5/) < £ Y. 54. 2] (The method of continuity). Let X,Y be Banach spaces and LQ,LI e £(X,Y). Lt := (1 - t)L0 + tLi Furthermore, let Vt e [0,1] and suppose that there exist a constant c such that \\u\\x

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