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Double phase anisotropic variational problems involving critical growth

Ky HoYun-Ho KimChao Zhang
Dec 2022
摘要
In this paper, we investigate some existence results for double phaseanisotropic variational problems involving critical growth. We first establisha Lions type concentration-compactness principle and its variant at infinityfor the solution space, which are our independent interests. By employing theseresults, we obtain a nontrivial nonnegative solution to problems of generalizedconcave-convex type. We also obtain infinitely many solutions when thenonlinear term is symmetric. Our results are new even for the$p(\cdot)$-Laplace equations.
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