## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Periodic solutions for second order Hamiltonian systems with general superquadratic potential

#### Abstract

In this paper, we study the existence of nontrivial solutions and ground state solutions for the second order Hamiltonian systems: $$\ddot u(t)+A(t)u(t)+\nabla F(t,u(t))=0\ \ \ \ \ \ \mbox{a.e. } t\in [0,T],$$ where $A(t)$ is a $N\times N$ symmetric matrix, continuous and $T$-periodic in $t$. Replacing the classical Ambrosetti-Rabinowitz superquadratic condition by a general superquadratic condition, we prove some existence theorems, which unify and improve some recent results in the literature.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 1 (2014), 1-18.

Dates
First available in Project Euclid: 11 March 2014

https://projecteuclid.org/euclid.bbms/1394544291

Digital Object Identifier
doi:10.36045/bbms/1394544291

Mathematical Reviews number (MathSciNet)
MR3178527

Zentralblatt MATH identifier
06291025

Subjects
Primary: 34C25: Periodic solutions

#### Citation

Ye, Yiwei; Tang, Chun-Lei. Periodic solutions for second order Hamiltonian systems with general superquadratic potential. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 1, 1--18. doi:10.36045/bbms/1394544291. https://projecteuclid.org/euclid.bbms/1394544291