Non-degeneracy and uniqueness of periodic solutionsfor $2n$-order differential equations

Pedro J. Torres; Zhibo Cheng; Jingli Ren

doi:10.3934/dcds.2013.33.2155

Article Contents

2013, Volume 33, Issue 5: 2155-2168. Doi: 10.3934/dcds.2013.33.2155

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Non-degeneracy and uniqueness of periodic solutions for $2n$-order differential equations

1.
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada
2.
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454000
3.
Dept. of Math., Zhengzhou University, Zhengzhou 450001

Received: December 2011

Revised: August 2012

Published: May 2013

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Abstract

We analyze the non-degeneracy of the linear $2n$-order differential equation $u^{(2n)}+\sum\limits_{m=1}^{2n-1}a_{m}u^{(m)}=q(t)u$ with potential $q(t)\in L^p(\mathbb{R}/T\mathbb{Z})$, by means of new forms of the optimal Sobolev and Wirtinger inequalities. The results is applied to obtain existence and uniqueness of periodic solution for the prescribed nonlinear problem in the semilinear and superlinear case.

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Mathematics Subject Classification: 34C25.

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References

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