Some one-dimensional elliptic problems with constraints
| Autor: | Schino, Jacopo, Smyrnelis, Panayotis |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given $m \in \mathbb{N} \setminus \{0\}$ and $\rho > 0$, we find solutions $(\lambda,u)$ to the problem \begin{equation*} \begin{cases} \bigl(-\frac{\mathrm{d}^2}{\mathrm{d} x^2}\bigr)^m u + \lambda G'(u) = F'(u)\\ \int_{\mathbb{R}} K(u) \, \mathrm{d}x = \rho \end{cases} \end{equation*} in the following cases: $m=1$ or $2G(s) = K(s) = s^2$. In the former, we follow a bifurcation argument; in the latter, we use variational methods. Comment: 17 pages |
| Databáze: | arXiv |
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