论文标题
涉及临界增长的双期各向异性变分问题
Double phase anisotropic variational problems involving critical growth
论文作者
论文摘要
在本文中，我们研究了涉及关键生长的双期各向异性变异问题的一些存在结果。我们首先建立了狮子型浓度 - 元素原理及其在溶液空间中的无穷大的变体，这是我们独立的利益。通过采用这些结果，我们可以为广义凹形凸型类型的问题获得非平凡的非负解决方案。当非线性项为对称时，我们还获得了无限的许多解决方案。即使对于$ p（\ cdot）$ - 拉普拉斯方程，我们的结果也是新的。
In this paper, we investigate some existence results for double phase anisotropic variational problems involving critical growth. We first establish a Lions type concentration-compactness principle and its variant at infinity for the solution space, which are our independent interests. By employing these results, we obtain a nontrivial nonnegative solution to problems of generalized concave-convex type. We also obtain infinitely many solutions when the nonlinear term is symmetric. Our results are new even for the $p(\cdot)$-Laplace equations.
