论文标题
存在略微批评纯净的诺伊曼问题的解决方案
Existence of solutions to a slightly supercritical pure Neumann problem
论文作者
论文摘要
我们显示了将固定溶液集中到纯净的neumann略微临界问题的存在和多样性。这是超临界制度中这种问题的第一个存在结果。由于解决方案必须满足零平均值的兼容性条件，因此所有解决方案都必须更改符号。我们的证明是基于Lyapunov-Schmidt还原参数，该参数结合了使用合适的对称性的零平均条件。我们的方法还保证了对Annuli中亚批判性诺伊曼问题的存在和多样性。还讨论了更通用的对称域（例如椭圆形）。
We show the existence and multiplicity of concentrating solutions to a pure Neumann slightly supercritical problem in a ball. This is the first existence result for this kind of problems in the supercritical regime. Since the solutions must satisfy a compatibility condition of zero average, all of them have to change sign. Our proofs are based on a Lyapunov-Schmidt reduction argument which incorporates the zero-average condition using suitable symmetries. Our approach also guarantees the existence and multiplicity of solutions to subcritical Neumann problems in annuli. More general symmetric domains (e.g. ellipsoids) are also discussed.
