Double phase anisotropic variational problems involving critical growth
Analysis of PDEs
2024-05-21 v2
Abstract
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 -Laplace equations.
Cite
@article{arxiv.2212.13505,
title = {Double phase anisotropic variational problems involving critical growth},
author = {Ky Ho and Yun-Ho Kim and Chao Zhang},
journal= {arXiv preprint arXiv:2212.13505},
year = {2024}
}