Spradlin, Gregory S. Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity. (English) Zbl 1065.34039 Electron. J. Differ. Equ. 2004, Paper No. 21, 13 p. (2004). 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 \(u\equiv 0\). Reviewer: Sergei Yu. Pilyugin (St. Petersburg) Cited in 5 Documents MSC: 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) Keywords:mountain pass theorem; variational methods; Nehari manifold; homoclinic solutions PDFBibTeX XMLCite \textit{G. S. Spradlin}, Electron. J. Differ. Equ. 2004, Paper No. 21, 13 p. (2004; Zbl 1065.34039) Full Text: EuDML EMIS