Existence of non-collision periodic solutions for second order singular dynamical systems

Shuqing Liang

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 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.

Keywords


Second order dynamical system; non-collision periodic solution; strong singularity; weak singularity; Schauder's fixed point theorem

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