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Multiple solutions for nonlinear periodic problems with discontinuities

Nikolaos S. Papageorgiou, Nikolaos Yannakakis (2002)

Archivum Mathematicum

In this paper we consider a periodic problem driven by the one dimensional p -Laplacian and with a discontinuous right hand side. We pass to a multivalued problem, by filling in the gaps at the discontinuity points. Then for the multivalued problem, using the nonsmooth critical point theory, we establish the existence of at least three distinct periodic solutions.

Multi-type synchronization of impulsive coupled oscillators via topology degree

Yingjie Bi, Zhidan Cai, Shuai Wang (2024)

Applications of Mathematics

The existence of synchronization is an important issue in complex dynamical networks. In this paper, we study the synchronization of impulsive coupled oscillator networks with the aid of rotating periodic solutions of impulsive system. The type of synchronization is closely related to the rotating matrix, which gives an insight for finding various types of synchronization in a united way. We transform the synchronization of impulsive coupled oscillators into the existence of rotating periodic solutions...

New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations

Yuji Liu, Xingyuan Liu (2013)

Mathematica Bohemica

This paper is a continuation of Y. Liu, Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695–720. By using Schaefer's fixed point theorem, new existence results on anti-periodic solutions of a class of nonlinear impulsive functional differential equations are established. The techniques to get the priori estimates of the possible solutions of the mentioned equations are different from those used in known papers. An example is...

New results on periodic solutions for a kind of Rayleigh equation

Mei-Lan Tang, Xin-Ge Liu, Xin-Bi Liu (2009)

Applications of Mathematics

The paper deals with the existence of periodic solutions for a kind of non-autonomous time-delay Rayleigh equation. With the continuation theorem of the coincidence degree and a priori estimates, some new results on the existence of periodic solutions for this kind of Rayleigh equation are established.

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