Electron. J. Diff. Equ., Vol. 2015 (2015), No. 238, pp. 1-14.

Fourth-order discrete anisotropic boundary-value problems

Maciej Leszczynski

In this article we consider the fourth-order discrete anisotropic boundary value problem with both advance and retardation. We apply the direct method of the calculus of variations and the mountain pass technique to prove the existence of at least one and at least two solutions. Non-existence of non-trivial solutions is also undertaken.

Submitted May 15, 2015. Published September 17, 2015.
Math Subject Classifications: 39A10.
Key Words: Discrete boundary value problem; critical point theory; discrete p-n-Laplacian; fourth-order.

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Maciej Leszczynski
Institute of Mathematics
Technical University of Lodz
Wolczanska 215, 90-924 Lodz, Poland
email: 165708@edu.p.lodz.pl

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