The existence of periodic solutions for nonconservative superlinear second order ODEs: a rotation number and spiral analysis approach

We investigate the existence of periodic solutions for nonconservative superlinear second-order differential equations in the sense of rotation numbers. Specifically, we focus on equations whose solutions at infinity behave comparably to a suitable linear system. By employing a rotation number approach, spiral analysis, and fixed-point theorems, we establish the existence of periodic solutions for nonconservative superlinear second-order differential equations. Among the equations we consider, a notable subclass is partially superlinear second-order differential equations, which provide a concrete illustration of our results. Our results extend several recent results, thereby advancing to a more comprehensive understanding of periodic behavior in nonconservative systems.