On sequences of large solutions for discrete anisotropic equations
In this paper, we determine a concrete interval of positive parameters $\lambda$, for which we prove the existence of infinitely many solutions for an anisotropic discrete Dirichlet problem \begin{align*} -\Delta\left( \alpha\left( k\right) |\Delta u(k-1)|^{p(k-1)-2}\Delta u(k-1)\right) =\lambda...
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2015-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3680 |
| Summary: | In this paper, we determine a concrete interval of positive parameters $\lambda$, for which we prove the existence of infinitely many solutions for an anisotropic discrete Dirichlet problem
\begin{align*}
-\Delta\left( \alpha\left( k\right) |\Delta u(k-1)|^{p(k-1)-2}\Delta u(k-1)\right) =\lambda f(k,u(k)),\quad k\in
\mathbb{Z}
\lbrack1,T],
\end{align*}
where the nonlinear term $f: \mathbb{Z} \lbrack1,T]\times \mathbb{R}\rightarrow\mathbb{R}$ has an appropriate behavior at infinity, without any symmetry assumptions. The approach is based on critical point theory. |
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| ISSN: | 1417-3875 |