## Rocky Mountain Journal of Mathematics

### Applications of variational methods to an anti-periodic boundary value problem of a second-order differential system

#### Abstract

In this paper, we discuss the existence of multiple solutions to a second order anti-periodic boundary value problem $\ddot {x}(t)+M x(t)+\nabla F(t, x(t))=0\quad\mbox{almost every } t\in [0, T],\\ x(0)=-x(T) \qquad\qquad\qquad\ \, \dot {x}(0)=-\dot {x}(T)$ by using variational methods and critical point theory. Furthermore, we obtain the existence of periodic solutions for corresponding second-order differential systems.

#### Article information

Source
Rocky Mountain J. Math., Volume 47, Number 5 (2017), 1721-1741.

Dates
First available in Project Euclid: 22 September 2017

https://projecteuclid.org/euclid.rmjm/1506045630

Digital Object Identifier
doi:10.1216/RMJ-2017-47-5-1721

Mathematical Reviews number (MathSciNet)
MR3705770

Zentralblatt MATH identifier
1385.34022

#### Citation

Tian, Yu; Zhang, Yajing. Applications of variational methods to an anti-periodic boundary value problem of a second-order differential system. Rocky Mountain J. Math. 47 (2017), no. 5, 1721--1741. doi:10.1216/RMJ-2017-47-5-1721. https://projecteuclid.org/euclid.rmjm/1506045630

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