Electron. J. Diff. Equ., Vol. 2013 (2013), No. 32, pp. 1-9.

Positive solutions for anisotropic discrete boundary-value problems

Marek Galewski, Szymon Glab, Renata Wieteska

Abstract:
Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution for anisotropic discrete Dirichlet boundary-value problems. Our results generalized and improve those in [16].

Submitted August 12, 2012. Published January 30, 2013.
Math Subject Classifications: 39A10, 34B18, 58E30.
Key Words: Discrete boundary value problem; mountain pass theorem; variational methods; Karush-Kuhn-Tucker Theorem; positive solution; anisotropic problem.

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Marek Galewski
Institute of Mathematics, Technical University of Lodz
Wolczanska 215, 90-924 Lodz, Poland
email: marek.galewski@p.lodz.pl
Szymon Glab
Institute of Mathematics, Technical University of Lodz
Wolczanska 215, 90-924 Lodz, Poland
email: szymon.glab@p.lodz.pl
Renata Wieteska
Institute of Mathematics, Technical University of Lodz
Wolczanska 215, 90-924 Lodz, Poland
email: renata.wieteska@p.lodz.pl

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