Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth
| Autor: | Edcarlos D. Silva, Marcos L. M. Carvalho, Claudiney Goulart |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Discrete & Continuous Dynamical Systems. 42:1039 |
| ISSN: | 1553-5231 1078-0947 |
| DOI: | 10.3934/dcds.2021146 |
| Popis: | It is established existence of solutions for subcritical and critical nonlinearities considering a fourth-order elliptic problem defined in the whole space \begin{document}$ \mathbb{R}^N $\end{document}. The work is devoted to study a class of potentials and nonlinearities which can be periodic or asymptotically periodic. Here we consider a general fourth-order elliptic problem where the principal part is given by \begin{document}$ \alpha \Delta^2 u + \beta \Delta u + V(x)u $\end{document} where \begin{document}$ \alpha > 0, \beta \in \mathbb{R} $\end{document} and \begin{document}$ V: \mathbb{R}^N \rightarrow \mathbb{R} $\end{document} is a continuous potential. Hence our main contribution is to consider general fourth-order elliptic problems taking into account the cases where \begin{document}$ \beta $\end{document} is negative, zero or positive. In order to do that we employ some fine estimates proving the compactness for the associated energy functional. |
| Databáze: | OpenAIRE |
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