Existence of non-collision periodic solutions for second order singular dynamical systems
KeywordsSecond order dynamical system, non-collision periodic solution, strong singularity, weak singularity, Schauder's fixed point theorem
AbstractIn 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 have 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.
How to Cite
LIANG, Shuqing. Existence of non-collision periodic solutions for second order singular dynamical systems. Topological Methods in Nonlinear Analysis [online]. 23 April 2010, T. 35, nr 1, s. 127–137. [accessed 1.2.2023].
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