Another multiplicity result for the periodic solutions of certain systems

Abstract

In this paper, we deal with a problem of the type $$\cases{(ϕ(u'))'=\nabla_xF(t,u) & in $[0,T]$\cr & \cr u(0)=u(T)\ , \hskip 3pt u'(0)=u'(T)\ ,\cr}$$ where, in particular, $\varphi$ is a homeomorphism from an open ball of ${\mathbf{R}}^n$ onto ${\mathbf{R}}^n$. Using the theory developed by Brezis and Mawhin in [1] jointly with our minimax theorem proved in [3], we obtain a general multiplicity result, under assumptions of qualitative nature only. Three remarkable corollaries are also presented.

References in corpus (1)

• On a minimax theorem: an improvement, a new proof and an overview of its applications

Cited by in corpus (2)

• An alternative theorem for gradient systems
• A more complete version of a minimax theorem