Multiplicity of positive periodic solutions of Rayleigh equations with singularities

Abstract

The existence of positive periodic solutions of the Rayleigh equations $ x''+f(x')+g(x) = e(t) $ with singularities is investigated in this paper. Based on the continuation theorem of coincidence degree theory and the method of upper and lower solutions, the multiple periodic solutions of the singular Rayleigh equations can be determined under the weak conditions of the term $ g $. We discuss both the repulsive singular case and the attractive singular case. Some results in the literature are generalized and improved. Moreover, some examples and numerical simulations are given to illustrate our theoretical analysis.

Keywords

• rayleigh equations
• singularities
• periodic solutions
• coincidence degree theory