Abstract
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.
Citation
Shuqing Liang. "Existence of non-collision periodic solutions for second order singular dynamical systems." Topol. Methods Nonlinear Anal. 35 (1) 127 - 137, 2010.
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