Multiplicity of positive periodic solutions to third-order variable coefficients singular dynamical systems

Abstract In this paper, by applying a nonlinear alternative principle of Leray–Schauder and Guo–Krasnosel’skii fixed point theorem on compression expansion cones, together with truncation technique, we study the existence multiplicity noncollision periodic solutions to third-order singular dynamical systems. By combining analysis sign Green’s function for linear equation, consider systems where potential has repulsive singularity at origin. The so-called strong force condition is not needed, nonlinearity may have changing behavior. Recent results in literature, even scalar case, are generalized improved.