论文标题
新的链接定理与对重要增长椭圆形问题的应用程序相关性非线性
New linking theorems with applications to critical growth elliptic problems with jumping nonlinearities
论文作者
论文摘要
我们研究跳跃非线性的关键生长椭圆问题。基于$ h^1_0（ω）$分解为$ - δ$的分解的标准链接参数不能用于获得此类问题的非平凡解决方案。我们表明，关联的变分函数基于$ h^1_0（ω）$的分组允许某些链接结构进入非线性submanifolds。为了捕获这些链接的几何形状，我们证明了不基于线性子空间的Rabinowitz定理的经典链接定理的几个概括。然后，我们使用这些新的链接定理来获得我们问题的非平凡解决方案。我们的抽象结果具有独立的兴趣，可用于获得跳跃非线性问题的其他类型问题的非平凡解决方案。
We study critical growth elliptic problems with jumping nonlinearities. Standard linking arguments based on decompositions of $H^1_0(Ω)$ into eigenspaces of $- Δ$ cannot be used to obtain nontrivial solutions to such problems. We show that the associated variational functional admits certain linking structures based on splittings of $H^1_0(Ω)$ into nonlinear submanifolds. In order to capture these linking geometries, we prove several generalizations of the classical linking theorem of Rabinowitz that are not based on linear subspaces. We then use these new linking theorems to obtain nontrivial solutions of our problems. Our abstract results are of independent interest and can be used to obtain nontrivial solutions of other types of problems with jumping nonlinearities as well.
