Topological Methods in Nonlinear Analysis
- Topol. Methods Nonlinear Anal.
- Volume 35, Number 1 (2010), 127-137.
Existence of non-collision periodic solutions for second order singular dynamical systems
In this paper, we study the existence of non-collision periodic solutions for the second order singular dynamical systems. We consider the systems where the potential has a repulsive or attractive type behavior near the singularity. The proof is based on Schauder's fixed point theorem involving a new type of cone. The so-called strong force condition is not needed and the nonlinearity could have sign changing behavior. We allow that the Green function is non-negative, so the critical case for the repulsive case is covered. Recent results in the literature are generalized and improved.
Topol. Methods Nonlinear Anal., Volume 35, Number 1 (2010), 127-137.
First available in Project Euclid: 21 April 2016
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Liang, Shuqing. Existence of non-collision periodic solutions for second order singular dynamical systems. Topol. Methods Nonlinear Anal. 35 (2010), no. 1, 127--137. https://projecteuclid.org/euclid.tmna/1461249005