Multiple Solutions of Nonlinear Boundary-value Problems for Ordinary Differential Equations
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We consider a Hamilton system related to the Trott curve in Harnack’s theorem. This theorem says that the maximal number of ovals for the fourth-order curve is four. We consider the related Hamilton system which has more ovals than prescribed by Harnack’s theorem. We give an explanation and consider the Dirichlet boundary-value problem for the system. Precise estimation is given for the number of solutions to the Dirichlet problem.
KeywordsPeriodic Solution Hamilton System Dirichlet Problem Phase Portrait Nontrivial Solution
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