Singularity problems to fourth-order Rayleigh equation with time-dependent deviating argument

• Main Authors: Yun Xin, Hongmin Liu
• Format: Article
• Language: English
• Published: SpringerOpen 2018-10-01
• Series: Advances in Difference Equations
• Subjects: Positive periodic solution; Fourth-order Rayleigh equation; Singularities of attractive and repulsive type; Time-dependent deviating argument
• Online Access: http://link.springer.com/article/10.1186/s13662-018-1799-0

Abstract The paper is devoted to an investigation of the existence of a positive periodic solution for a kind of fourth-order singular Rayleigh equation with time-dependent deviating argument, where the nonlinear term g satisfies singularities of attractive and repulsive type at the origin and has time-dependent deviating argument. By applications of coincidence degree theory, we prove that this equation has at least one positive periodic solution. At last, two examples are given to show applications of theorems.