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# Double phase anisotropic variational problems involving critical growth

Dec 2022

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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