Open Access Research

Boundedness of solutions for a class of second-order differential equation with singularity

Shunjun Jiang

Author Affiliations

College of Sciences, Nanjing University of Technology, Nanjing, 210009, People’s Republic of China

Boundary Value Problems 2013, 2013:84  doi:10.1186/1687-2770-2013-84

Published: 10 April 2013

Abstract

In this paper, we study the following second-order periodic system:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/84/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/84/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/84/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/84/mathml/M2">View MathML</a> has a singularity. Under some assumptions on the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/84/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/84/mathml/M2">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/84/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/84/mathml/M4">View MathML</a> by Ortega’s small twist theorem, we obtain the existence of quasi-periodic solutions and boundedness of all the solutions.

Keywords:
boundedness of solutions; singularity; small twist theorem