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.
Citation
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
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