Abstract
AbstractSemilinear equations of Boussinesq type, e.g. utt + uxx − uxxxx + (u2)xx = 0, utt + uxx − uxxxx + uxuxx = 0, or certain equations containing the squared wave operator, e.g. uxxtt − uk = 0, k ϵ N k ≥ 2, are studied. A generalized boundary value problem on bounded domains can be treated using Hilbert space methods. The linear parts of these equations are not elliptic, the latter not even hypoelliptic. A mountain pass lemma is used to prove the existence of nontrivial weak solutions. These solutions are obtained in anisotropic Sobolev spaces.
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