Periodic solutions of singular second order equations at resonance

Abstract

In this paper, we study the existence of positive periodic solutions for singular second order equationswhere h has a singularity at the origin and n is a positive integer. We give an explicit condition to ensure the existence of positive periodic solutions when h is an unbounded perturbation at infinity by using qualitative analysis and topological degree theory.

New approach to the singular solution of implicit ordinary differential equations

“…In addition, singularity problems in partial differential equation have brought about the widespread attention in the field of applied sciences, such as nonlinear elasticity [8], Bose-Einstein condensate [21] and so on. Unfortunately, it is impossible to determine the singular solution only by the general solution structure according to the definition for these partial differential equations, let alone to find their possible singular periodic solutions [22] [23], which play important roles in the studying of the Lyapunov stability of dynamical systems [6].…”