<abstract xmlns="http://www.w3.org/1999/xhtml"> In this article we consider equations of the type <italic>x</italic>ʺ+g(x) = 0 and <italic>x</italic>ʺ+ƒ(x)<italic>x</italic>ʹ&lt;sup>2&lt;/sup> + <italic>g</italic>(<italic>x</italic>) = 0. The Neumann boundary value problem is considered. For polynomials <italic>f </italic>and <italic>g </italic>we provide the multiplicity results. These results are based on a thorough analysis of a phase plane. The existence of period annuli is concerned.</abstract>

In this article we consider equations of the type xʺ+g(x) = 0 and xʺ+ƒ(x)xʹ2 + 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.

Period annuli and multiple solutions for two-point BVD

Daugavpils University Department of Mathematics and Natural Sciences Parades iela 1 LV–5400 Daugavpils LATVIA

Tatra Mountains Mathematical Publications

{"article-title":"Period annuli and multiple solutions for two-point BVD"}

In this article we consider equations of the type xʺ+g(x) = 0 and xʺ+ƒ(x)xʹ2 + 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.

In this article we consider equations of the type xʺ+g(x) = 0 and xʺ+ƒ(x)xʹ2 + g(x) = 0. The Neumann boundary value problem is considered. For...

Period annuli and multiple solutions for two-point BVD

Published Online: Nov 12, 2012

Page range: 11 - 23

DOI: https://doi.org/10.2478/v10127-009-0021-x

Keywords
Neumann boundary conditions, phase portrait, period annulus, multiplicity of solutions.

This content is open access.

Period annuli and multiple solutions for two-point BVD

Published Online: Nov 12, 2012

Page range: 11 - 23

DOI: https://doi.org/10.2478/v10127-009-0021-x

KeywordsNeumann boundary conditions, phase portrait, period annulus, multiplicity of solutions.

This content is open access.

Keywords
Neumann boundary conditions, phase portrait, period annulus, multiplicity of solutions.