论文标题
准线性椭圆运算符的非线性特征值问题和分叉
Nonlinear eigenvalue problems and bifurcation for quasi-linear elliptic operators
论文作者
论文摘要
在本文中，我们分析了在开放的平滑界面域中涉及均匀的Dirichlet边界条件的准线性椭圆算子的特征值问题。我们表明，与特征值相对应的特征函数属于$ l^{\ infty} $，这意味着$ c^{1，α} $平滑度，而第一个特征值很简单。此外，我们使用Krasnoselski分叉定理研究了琐碎溶液的分叉化结果，并使用Leray-Schauder学位研究了无穷大。我们还使用变分方法和Krasnoselski属显示了多个临界点的存在。
In this paper, we analyze an eigenvalue problem for quasi-linear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We show that the eigenfunctions corresponding to the eigenvalues belong to $L^{\infty}$, which implies $C^{1,α}$ smoothness, and the first eigenvalue is simple. Moreover, we investigate the bifurcation results from trivial solutions using the Krasnoselski bifurcation theorem and from infinity using the Leray-Schauder degree. We also show the existence of multiple critical points using variational methods and the Krasnoselski genus.
