On critical double phase problems in $\mathbb{R}^N$ involving variable exponents

Hoang Hai Ha; Ky Ho

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arXiv · 2405.11774

On critical double phase problems in $\mathbb{R}^N$ involving variable exponents

Hoang Hai Ha·Ky Ho

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Abstract

We establish a Lions-type concentration-compactness principle and its variant at infinity for Musielak-Orlicz-Sobolev spaces associated with a double phase operator with variable exponents. Based on these principles, we demonstrate the existence and concentration of solutions for a class of critical double phase equations of Schr\"odinger type in $\mathbb{R}^N$ involving variable exponents with various types of potentials. Our growth condition is more appropriately suited compared to the existing works.

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Hoang Hai Ha, Ky Ho. 2024-05-20. On critical double phase problems in $\mathbb{R}^N$ involving variable exponents. https://arxiv.org/abs/2405.11774

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