On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems

Abstract

Abstract In this paper, we prove a new quantitative deformation lemma, and then gain a new mountain pass theorem in Hilbert spaces. By using the new mountain pass theorem, we obtain the new existence of two nontrivial periodic solutions for a class of nonlinear second-order discrete systems, which greatly improves the result in (Zhou et al. in Proc. R. Soc. Edinb. A 134:1013–1022, 2004).

Keywords

• Critical points
• Quantitative deformation lemma
• Mountain pass theorem
• Nontrivial periodic solutions
• Discrete systems