Electron. J. Differential Equations,
Vol. 2017 (2017), No. 228, pp. 112.
Sequences of small homoclinic solutions for difference equations
on integers
Robert Steglinski
Abstract:
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 [11].
Submitted July 18, 2017. Published September 22, 2017.
Math Subject Classifications: 39A10, 47J30, 35B38.
Key Words: Difference equations; discrete pLaplacian; variational methods;
infinitely many solutions.
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Robert Steglinski
Institute of Mathematics
Lodz University of Technology
Wolczanska 215, 90924 Lodz, Poland
email: robert.steglinski@p.lodz.pl

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