Exact Multiplicity and Stability of Periodic Solutions for Duffing Equation with Bifurcation Method

摘要

Under some L-p-norms(p is an element of[1, infinity]) assumptions for the derivative of the restoring force, the exact multiplicity and the stability of 2 pi-periodic solutions for Duffing equation are considered. The nontrivial 2 pi-periodic solutions of it are positive or negative, and the bifurcation curve of it is a unique reversed S-shaped curve. The class of the restoring force is extended, comparing with the class of L-infinity-norm condition. The proof is based on the global bifurcation theorem, topological degree and the estimates for periodic eigenvalues of Hill's equation by L-p-norms(p is an element of[1, infinity]).