A Landesman-Lazer type condition for second-order differential equations with a singularity at resonance

Abstract

In this paper, we are concerned with the existence of positive periodic solutions for second-order differential equations with a singularity at resonance. A Landesman-Lazer type condition is given to obtain the existence of positive periodic solutions using phase-plane analysis method and topological degree method.

Keywords:

• periodic solutions
• singularity
• at resonance
• Landesman-Lazer type condition

AMS Subject Classifications:

• 34C25
• 34D40

Acknowledgements

The authors would like to express their thanks to the editor of the journal and the anonymous referees for their carefully reading of the first draft of the manuscript and making many helpful comments and suggestions which improved the presentation of the paper.

Additional information

Funding

Research supported by National Natural Science Foundation of China [grant number 11401274]; Science and technology landing project of colleges and universities in Jiangxi Province [grant number KJLD14092]; Research Fund for the Doctoral Program of Higher Education of China [grant number 11AA0013]; Beijing Natural Science Foundation (Existence and multiplicity of periodic solutions in nonlinear oscillations) [grant number 1112006] and the grant of Beijing Education Committee Key Project [grant number KZ201310028031].