Abstract
Abstract In this article we consider equations of the type xʺ+g(x) = 0 and xʺ+ƒ(x)xʹ<sup>2</sup> + g(x) = 0. The Neumann boundary value problem is considered. For polynomials f and g 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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