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.
Highlights
Applying the limit properties of time map, the authors obtained the existence of periodic solution for this equation
In the following, applying Lemma 2.1, we prove the existence of a periodic solution for equation (1.1) with singularity of repulsive type
3 Periodic solution for equation (1.1) in the case that p = 2 In the following, by Lemma 2.1 and Theorem 2.1, we prove the existence of a periodic solution for equation (1.1) with singularity of repulsive type
Summary
Li and Ge’s work [18] has been performed on the existence of a periodic solution of equation (1.1) with strong singularity of repulsive type by using Manásevich–Mawhin continuation theorem, where p = 2, g satisfied a semilinear condition and equation (1.2). Applying the extension of Mawhin’s continuation theorem, equation (2.1) has at least one T-periodic solution. In the following, applying Lemma 2.1, we prove the existence of a periodic solution for equation (1.1) with singularity of repulsive type.
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