Periodic solution for prescribed mean curvature Rayleigh equation with a singularity

Abstract

In this paper, we consider the existence of a periodic solution for a prescribed mean curvature Rayleigh equation with singularity (weak and strong singularities of attractive type or weak and strong singularities of repulsive type). Our proof is based on an extension of Mawhin’s continuation theorem.

Positive periodic solutions for a $\phi$-Laplacian generalized Rayleigh equation with a singularity

“…At the same time, Rayleigh equations with a singularity were also explored by authors [14,15,16,17,18,19,20,21]. For example, Lu et al [18] discussed p-Laplacian Rayleigh equations with a singularity in 2016 as follows:…”

An exact expression of positive periodic solution for a first-order singular equation

“…As is well known, singular equations have a wide range of applications in many fields, and the existence of positive ω-periodic solutions to singular equations plays a significant role in solving many practical problems. There is a good amount of work on periodic solutions for singular equations (see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references cited therein). In 2003, Agarwal and O'Regan [4] provided some results on positive ω-periodic solutions of Eq.…”

Weak and strong singularities problems to Liénard equation

“…Lazer and Solimini's work has attracted the attention of many scholars in singular equations. More recently, the Poincaré-Birkhoff twist theorem [2][3][4], Schauder's fixed point theorem [5][6][7][8], the Leray-Schauder alternative principle [9][10][11], coincidence degree theory [12][13][14][15],the Krasnoselskii fixed point theorem in cones [16,17] and Leray-Schauder degree theory [18,19] have been employed to discuss the existence of a positive periodic solution of singular equations.…”