| Autor: |
Giovanni Anello, Filippo Cammaroto, Luca Vilasi |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2022, Iss 32, Pp 1-12 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
1417-3875 |
| DOI: |
10.14232/ejqtde.2022.1.32 |
| Popis: |
We examine the semilinear resonant problem $$ -\Delta u = \lambda_1 u + \lambda g(u) \quad \text{in } \Omega,\ u\geq 0 \text{ in } \Omega, \ u_{|\partial\Omega}=0, $$ where $\Omega\subset\mathbb R^N$ is a smooth, bounded domain, $\lambda_1$ is the first eigenvalue of $-\Delta$ in $\Omega$, $\lambda>0$. Inspired by a previous result in literature involving power-type nonlinearities, we consider here a generic sublinear term $g$ and single out conditions to ensure: the existence of solutions for all $\lambda>0$; the validity of the strong maximum principle for sufficiently small $\lambda$. The proof rests upon variational arguments. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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