Monotonicity of positive solutions for an indefinite logarithmic Laplacian equation
| Autor: | Liu, Baiyu, Xu, Shasha |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we investigate a nonlocal equation involving the logarithmic Laplacian with indefinite nonlinearities: \begin{equation*} \left\{ \begin{array}{ll} L_\Delta u(x)=a(x_n)f(u), & x\in\Omega, \\ u(x)=0,& x\in \mathbb{R}^n\backslash\Omega. \end{array} \right. \end{equation*} Here, $\Omega$ represents a Lipschitz coercive epigraph. To achieve our objectives, we develop a boundary estimate for antisymmetric functions, enabling us to establish the monotonicity and nonexistence of bounded positive solutions for the above problem using the direct method of moving planes. Comment: 24 pages, 9 figures |
| Databáze: | arXiv |
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