Solutions of two-point boundary value problems via phase-plane analysis

Svetlana Atslega, F. Sadyrbaev
2016 Proceedings of The 10'th Colloquium on the Qualitative Theory of Differential Equations (July 1–4, 2015, Szeged, Hungary) edited by: T. Krisztin   unpublished
We consider period annuli (continua of periodic solutions) in equations of the type x + g(x) = 0 and x + f (x)x 2 + g(x) = 0, where g and f are polynomials. The conditions are provided for existence of multiple nontrivial (encircling more than one critical point) period annuli. The conditions are obtained (by phase-plane analysis of period annuli) for existence of families of solutions to the Neumann boundary value problems.
doi:10.14232/ejqtde.2016.8.4 fatcat:lhycyj3ofbes7e23rtwh5d4qi4