# American Institute of Mathematical Sciences

2013, 2013(special): 759-769. doi: 10.3934/proc.2013.2013.759

## Existence of solutions to a multi-point boundary value problem for a second order differential system via the dual least action principle

 1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China 2 Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States

Received  September 2012 Published  November 2013

In this paper, by using the dual least action principle, the authors investigate the existence of solutions to a multi-point boundary value problem for a second-order differential system with $p$-Laplacian.
Citation: Yu Tian, John R. Graef, Lingju Kong, Min Wang. Existence of solutions to a multi-point boundary value problem for a second order differential system via the dual least action principle. Conference Publications, 2013, 2013 (special) : 759-769. doi: 10.3934/proc.2013.2013.759
##### References:
 [1] J. R. Graef, S. Heidarkhani, and L. Kong, Infinitely many solutions for systems of multi-point boundary value problems,, Topol. Methods Nonlinear Anal. 42 (2013), 42 (2013), 105.   Google Scholar [2] J. R. Graef, S. Heidarkhani, and L. Kong, A critical points approach to multiplicity results for multi-point boundary value problems,, Appl. Anal. 90 (2011), 90 (2011), 1909.   Google Scholar [3] J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems,, Springer-Verlag, (1989).   Google Scholar [4] C. Tang, Periodic solutions for nonautomous second order systems with sublinear nonlinearity,, Proc. Amer. Math. Soc. 126 (1998), 126 (1998), 3263.   Google Scholar [5] Y. Tian and W. Ge, Periodic solutions of non-autonomous second-order systems with a p-Laplacian,, Nonlinear Anal. 66 (2007) 192-203., 66 (2007), 192.   Google Scholar [6] Y. Tian and W. Ge, Applications of variational methods to boundary value problem for impulsive differential equations,, Proc. Edin. Math. Soc. 51 (2008) 509-527., 51 (2008), 509.   Google Scholar

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##### References:
 [1] J. R. Graef, S. Heidarkhani, and L. Kong, Infinitely many solutions for systems of multi-point boundary value problems,, Topol. Methods Nonlinear Anal. 42 (2013), 42 (2013), 105.   Google Scholar [2] J. R. Graef, S. Heidarkhani, and L. Kong, A critical points approach to multiplicity results for multi-point boundary value problems,, Appl. Anal. 90 (2011), 90 (2011), 1909.   Google Scholar [3] J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems,, Springer-Verlag, (1989).   Google Scholar [4] C. Tang, Periodic solutions for nonautomous second order systems with sublinear nonlinearity,, Proc. Amer. Math. Soc. 126 (1998), 126 (1998), 3263.   Google Scholar [5] Y. Tian and W. Ge, Periodic solutions of non-autonomous second-order systems with a p-Laplacian,, Nonlinear Anal. 66 (2007) 192-203., 66 (2007), 192.   Google Scholar [6] Y. Tian and W. Ge, Applications of variational methods to boundary value problem for impulsive differential equations,, Proc. Edin. Math. Soc. 51 (2008) 509-527., 51 (2008), 509.   Google Scholar
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