In this paper, we consider a class of semilinear elliptic equation with critical exponent and -1 growth. By using the critical point theory for nonsmooth functionals, two positive solutions are obtained. Moreover, the symmetry and monotonicity properties of the solutions are proved by the moving plane method. Our results improve the corresponding results in the literature.

中文翻译：

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一类具有临界指数和-1增长的椭圆问题的正径向对称解

在本文中，我们考虑一类具有临界指数和-1增长的半线性椭圆方程。通过将临界点理论用于非光滑泛函，可以获得两个正解。此外，通过移动平面法​​证明了溶液的对称性和单调性。我们的结果改进了文献中的相应结果。