论文标题
$ ϕ $ -LAPLACIAN运算符的绑定设置
Bound sets for a class of $ϕ$-Laplacian operators
论文作者
论文摘要
我们将Hartman-Knobloch定理的扩展为vector差速度系统的定期解决方案到一般类别的$ ϕ $ -laplacian差异操作员。我们的主要工具是为该类的操作员方程开发的Manásevich-Mawhin持续定理的变体，以及界集理论。我们的结果涉及凸面结合集的情况，我们使用由于Krantz和Parks引起的Sublevel集合的特征来显示一些新的连接。我们还扩展到$ ϕ $ -LAPLACIAN矢量案例，是标量定期扰动的Liénard方程的Reissig的经典定理。
We provide an extension of the Hartman-Knobloch theorem for periodic solutions of vector differential systems to a general class of $ϕ$-Laplacian differential operators. Our main tool is a variant of the Manásevich-Mawhin continuation theorem developed for this class of operator equations, together with the theory of bound sets. Our results concern the case of convex bound sets for which we show some new connections using a characterisation of sublevel sets due to Krantz and Parks. We also extend to the $ϕ$-Laplacian vector case a classical theorem of Reissig for scalar periodically perturbed Liénard equations.
