Existence of periodic solutions for second-order differential equations with singularities and the strong force condition

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• 作者：Rogé ; rio Ferreira Martins
• 关键词：Periodic solutions ; Subharmonics ; Repulsive singularities ; Truncation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2006
• 出版时间：1 May 2006
• 年：2006
• 卷：317
• 期：1
• 页码：1-13
• 全文大小：110 K

文摘

We prove the existence of periodic solutions for the equation

where the nonlinearity g has a repulsive singularity at the origin. In previous papers dealing with this kind of problem it is usually assumed a nonintegrability condition on g near the origin. We provide a weaker condition that substitutes the nonintegrability of g. If f≡0 the existence of subharmonic solutions is proved utilizing a variational method and when f≠0 we prove the existence of a periodic solution using topological degree theory.