Sequences of small homoclinic solutions for difference equations on integers
In this article, we determine a concrete interval of positive parameters $\lambda $, for which we prove the existence of infinitely many homoclinic solutions for a discrete problem $$ -\Delta \big( a(k)\phi _{p}(\Delta u(k-1))\big) +b(k)\phi_{p}(u(k)) =\lambda f(k,u(k)),\quad k\in \mathbb{Z},...
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/228/abstr.html |
| Summary: | In this article, we determine a concrete interval of positive parameters
$\lambda $, for which we prove the existence of infinitely many homoclinic
solutions for a discrete problem
$$
-\Delta \big( a(k)\phi _{p}(\Delta u(k-1))\big) +b(k)\phi_{p}(u(k))
=\lambda f(k,u(k)),\quad k\in \mathbb{Z},
$$
where the nonlinear term $f:\mathbb{Z}\times \mathbb{R} \to \mathbb{R}$
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]. |
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| ISSN: | 1072-6691 |