Period annuli and multiple solutions for two-point BVP

Svetlana Atslega, Felikss Sadyrbaev


In this article we consider equations of the type
$x''+g(x)=0$ and $x''+ f(x) x'^2 + g(x)=0.$ The Neumann boundary
value problem is considered. For $f$ and $g$ polynomials we
provide the multiplicity results. These results are based on a
thorough analysis of a phase plane. The existence of period annuli
is concerned.

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