Global solution curves for several classes of singular periodic problems

TL;DR

This paper investigates the global structure and multiplicity of periodic solutions in singular periodic problems across various fields using bifurcation theory and continuation methods.

Contribution

It provides a comprehensive analysis of the solution structure for three classes of singular periodic equations, including applications in MEMS and physics.

Findings

Identified multiple periodic solutions in singular problems

Mapped the global solution structure for different classes

Applied bifurcation theory to complex singular equations

Abstract

Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for three classes of periodically forced equations with singularities, including the equations arising in micro-electro-mechanical systems (MEMS), the ones in condensed matter physics, as well as A.C. Lazer and S. Solimini's \cite{LS} problem.