论文标题
半线性分数诺伊曼问题的存在和不存在结果
Existence and non-existence results for a semilinear fractional Neumann problem
论文作者
论文摘要
我们建立了一个先验的$ l^\ infty $估计，用于半固有非本地诺伊曼问题的非负解决方案。由于这些估计值，我们在适当的扩散系数和非线性的假设下不存在非恒定溶液的不存在。此外，在可能的超临界非线性的情况下，我们证明了径向，径向非压缩的解决方案的存在，并扩展到$ 0 <s \ le 1/2 $ [7]中的分析开始。
We establish a priori $L^\infty$-estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion coefficient and on the nonlinearity. Moreover, we prove an existence result for radial, radially non-decreasing solutions in the case of a possible supercritical nonlinearity, extending to the case $0<s\le 1/2$ the analysis started in [7].
