Convex radial solutions for Monge-Ampère equations involving the gradient
| Autor: | Zhilin Yang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Mathematical Biosciences and Engineering, Vol 20, Iss 12, Pp 20959-20970 (2023) |
| Druh dokumentu: | article |
| ISSN: | 1551-0018 |
| DOI: | 10.3934/mbe.2023927?viewType=HTML |
| Popis: | This paper deals with the existence and multiplicity of convex radial solutions for the Monge-Amp$ \grave{\text e} $re equation involving the gradient $ \nabla u $: $ \begin{cases} \det (D^2u) = f(|x|, -u, |\nabla u|), x\in B, \\ u|_{\partial B} = 0, \end{cases} $ where $ B: = \{x\in \mathbb R^N: |x| < 1\} $. The fixed point index theory is employed in the proofs of the main results. |
| Databáze: | Directory of Open Access Journals |
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