Exact multiplicity and stability of periodic solutions for a Duffing equation
The aim of this paper is to prove new results on the exact multiplicity and stability of \(2\pi\)-periodic solutions of the damped Duffing equation \[ x''+cx'+g(t,x)=h(t). \] The proof is based on a known connection between stability and topological index (see, for instance, [\textit{R. Ortega}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 472, 377--409 (1995; Zbl 0834.34058)]), together with some delicate \(L^p\) estimates for periodic and antiperiodic eigenvalues by \textit{M. Zhang} and \textit{W. Li} [Proc. Am. Math. Soc. 130, No. 11, 3325--3333 (2002; Zbl 1007.34053)].
scientific article; zbMATH DE number 6147181
scientific article