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Non-existence and uniqueness results for fourth-order Hamiltonian systems

We give a classification of all bounded solutions of the equation u´´´´ + pu´´ + F´(u) = 0, - < t < , in which F is a general quartic polynomial and p is restricted to various subsets of (-,0]. These results are obtained by combining an a priori estimate with geometric arguments in the (u,u´´)-plane.