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Mathematics 2019, 7(3), 276; https://doi.org/10.3390/math7030276

Variational Approaches for Lagrangian Discrete Nonlinear Systems

1
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
2
Faculty of Basic Sciences, Babol (Noushirvani) University of Technology, Babol, Iran
*
Author to whom correspondence should be addressed.
Received: 21 January 2019 / Revised: 10 March 2019 / Accepted: 12 March 2019 / Published: 18 March 2019
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PDF [265 KB, uploaded 18 March 2019]

Abstract

In this paper, we study the multiple solutions for Lagrangian systems of discrete second-order boundary value systems involving the discrete p-Laplacian operator. The technical approaches are based on a local minimum theorem for differentiable functionals in a finite dimensional space and variational methods due to Bonanno. The existence of at least one solution, as well as three solutions for the given system are discussed and some examples and remarks have also been given to illustrate the main results. View Full-Text
Keywords: discrete second order boundary value system; multiple solutions; critical point theory; Lipschitz condition; discrete p-Laplacian operator; Lagrangian discrete system discrete second order boundary value system; multiple solutions; critical point theory; Lipschitz condition; discrete p-Laplacian operator; Lagrangian discrete system
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Alkhalidi, A.A.H.; Afrouzi, G.A.; Khademloo, S. Variational Approaches for Lagrangian Discrete Nonlinear Systems. Mathematics 2019, 7, 276.

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