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Non-existence and uniqueness results for fourth-order Hamiltonian systems. (English) Zbl 0934.37050
The main goal of this paper is to study the solution set of the equation $$u''''+ pu''+ F'(u)=0, \qquad -\infty< t< \infty, \quad p\leq 0.$$ The author is interested in potentials $F$ that have one or two wells. The main results of this paper are based on combining an a priori estimate with geometric arguments in the $(u,u'')$-plane, so-called pseudo-phase plane concept. A particularly interesting application is the change in the bifurcation diagram.

37J05Relations of dynamical systems with symplectic geometry and topology
37J20Bifurcation problems (finite-dimensional Hamiltonian etc. systems)
34A99General theory of ODE
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