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2017 Applications of variational methods to an anti-periodic boundary value problem of a second-order differential system
Yu Tian, Yajing Zhang
Rocky Mountain J. Math. 47(5): 1721-1741 (2017). DOI: 10.1216/RMJ-2017-47-5-1721

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.

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Yu Tian. Yajing Zhang. "Applications of variational methods to an anti-periodic boundary value problem of a second-order differential system." Rocky Mountain J. Math. 47 (5) 1721 - 1741, 2017. https://doi.org/10.1216/RMJ-2017-47-5-1721

Information

Published: 2017
First available in Project Euclid: 22 September 2017

zbMATH: 1385.34022
MathSciNet: MR3705770
Digital Object Identifier: 10.1216/RMJ-2017-47-5-1721

Subjects:
Primary: 34B15 , 58E30

Keywords: Anti-periodic boundary value problem , Mountain pass theorem , variational methods

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 5 • 2017
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