Zhenhui Wang, Zhibo Cheng, Positive periodic solutions for a $\phi$-Laplacian generalized Rayleigh equation with a singularity, Vol. 2023 (2023), Article ID 31, pp. 1-7

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DOI: 10.23952/jnfa.2023.31

Received January 11, 2023; Accepted September 6, 2023; Published October 10, 2023

Abstract. This paper explores the existence of positive periodic solutions to a $\phi$ -Laplacian generalized Rayleigh equation with a singularity as $(\phi(v'(t)))'+f(t,v'(t))+g(v(t))=e(t),$ where the function $g$ has a repulsive singularity at $v=0$ . According to the Manásevich-Mawhin continuation theorem, we prove the existence of positive periodic solutions to this equation. This result is feasible for the cases of a strong or weak singularity.

How to Cite this Article:
Z. Wang, Z. Cheng, Positive periodic solutions for a $\phi$ -Laplacian generalized Rayleigh equation with a singularity, J. Nonlinear Funct. Anal. 2023 (2023) 31.