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

Abstract

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

Keywords

• Singular
• Dynamical systems
• Leray–Schauder alternative principle
• Guo–Krasnosel’skii fixed point theorem