Journal of Mathematical Sciences

, Volume 205, Issue 6, pp 768–776 | Cite as

Multiple Solutions of Nonlinear Boundary-value Problems for Ordinary Differential Equations


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.


Periodic Solution Hamilton System Dirichlet Problem Phase Portrait Nontrivial Solution 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Daugavpils UniversityDaugavpilsLatvia

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