In this article, we determine a concrete interval of positive parameters , for which we prove the existence of infinitely many homoclinic solutions for a discrete problem
where the nonlinear term has an appropriate oscillatory behavior at zero. We use both the general variational principle of Ricceri and the direct method introduced by Faraci and Kristaly .
Submitted July 18, 2017. Published September 22, 2017.
Math Subject Classifications: 39A10, 47J30, 35B38.
Key Words: Difference equations; discrete p-Laplacian; variational methods; infinitely many solutions.
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| Robert Steglinski |
Institute of Mathematics
Lodz University of Technology
Wolczanska 215, 90-924 Lodz, Poland
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