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Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity. (English) Zbl 1065.34039

Consider the system \[ -u''+u=g(t)V'(u), \] where \(u\) is a vector and \(V'\) is the gradient of a positive potential function similar to \(| q| ^p\) with \(p>2\). Sufficient conditions (too complicated to be stated here) are given under which there exists a nontrivial homoclinic solution to \(u\equiv 0\).

MSC:

34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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