Meirong Zhang

TL;DR: In this article, the authors established two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems, based on a nonlinear alternative principle of Leray-Schauder and Schauder's fixed point theorem.

TL;DR: In this article, it was proved that the singular perturbation problem has at least two positive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbations are superlinear at infinity.

TL;DR: In this paper, the authors used the coincidence degree to give an existence result of periodic solutions for the scalar Lienard equations with singular forces of repulsive type, and the main result clearly describes what balance conditions between the singular force at the singularity and at the infinity should be imposed if the equation has a periodic solution.

TL;DR: In this article, the periodic and anti-periodic eigenvalues of the one-dimensional p-Laplacian with a periodic potential were studied, and it was shown that for any non-negative integer n, the endpoints of the interval 1 (n=2) in R yield the corresponding periodic or antiperiodic Eigenvalues.

TL;DR: In this article, a relationship between the periodic and Dirichlet boundary value problems for second-order ODEs with singularities is established, which may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations.