Electron. J. Diff. Equ., Vol. 2014 (2014), No. 55, pp. 1-13.

Emden-Fowler problem for discrete operators with variable exponent

Maria Malin

In this article, we prove the existence of homoclinic solutions for a p(.)-Laplacian difference equation on the set of integers, involving a coercive weight function and a reaction term satisfying the Ambrosetti-Rabinowitz condition. The proof of the main result is obtained by using critical point theory combined with adequate variational techniques, which are mainly based on the mountain pass theorem.

Submitted December 8, 2013. Published February 25, 2014.
Math Subject Classifications: 39A14, 44A55, 34C375.
Key Words: Difference equations; discrete p(.)-Laplacian; homoclinic solution, mountain pass lemma.

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Maria Malin
Department of Mathematics
University of Craiova, 200585, Romania
email: amy.malin@yahoo.com

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