论文标题
在足够的“本地”条件下，存在的结果为广义$ p（\ cdot）$ - 拉普拉斯方程涉及关键增长
On sufficient "local" conditions for existence results to generalized $p(\cdot)$-Laplace equations involving critical growth
论文作者
论文摘要
在本文中，我们研究了对广义$ p（\ cdot）$ laplace方程的多种解决方案的存在，其中有两个涉及关键增长的参数。更确切地说，我们提供了足够的“本地”条件，这意味着对于$ p（\ cdot）$ - sublinear，$ p（\ cdot）$ - superlineare和sandwich-type，在本地假定了主要操作员和非线性术语之间的增长。与恒定的指数问题（示例，$ p $ -laplacian和$（p，q）$ - laplacian相比，这是对可变指数问题的研究的特征。我们通过应用$ p（\ cdot）$ - sublinear和$ p（\ cdot）$ - 超级线性案例的山脉定理的变体，并构建由三明治型案例的属理论中的minimax参数定义的关键值。此外，我们还获得了一种非平凡的非负解决方案，用于改变参数的作用。我们的工作是对文献中现有作品的概括。
In this paper, we study the existence of multiple solutions to a generalized $p(\cdot)$-Laplace equation with two parameters involving critical growth. More precisely, we give sufficient "local" conditions, which mean that growths between the main operator and nonlinear term are locally assumed for the cases $p(\cdot)$-sublinear, $p(\cdot)$-superlinear, and sandwich-type. Compared to constant exponent problems (for examples, $p$-Laplacian and $(p,q)$-Laplacian), this characterizes the study of variable exponent problems. We show this by applying variants of the Mountain Pass Theorem for $p(\cdot)$-sublinear and $p(\cdot)$-superlinear cases and constructing critical values defined by a minimax argument in the genus theory for sandwich-type case. Moreover, we also obtain a nontrivial nonnegative solution for sandwich-type case changing a role of parameters. Our work is a generalization of several existing works in the literature.
