On critical double phase problems in ℝ^N involving variable exponents

2024/05/20 by Hoang Hai Ha, Ky Ho, Ha, Hoang Hai +1
Computer Science · Mathematics · #35J20 #35J60 #35J70 #46E35 #47J10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2405.11774

openalex publication_date 2024/05/20 · openalex created_date 2024/05/22 · openalex updated_date 2026/07/28

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 Schrödinger type in 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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