Nabil Chems Eddine, Anass Ouannasser, Maria Alessandra Ragusa, On a new class of anisotropic double phase equations

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DOI: 10.23952/jnva.9.2025.3.02

Volume 9, Issue 3, 1 June 2025, Pages 329-355

Abstract. In this paper, we introduce a new class of anisotropic double phase equations with variable exponents. We establish several properties related to the anisotropic Musielak-Orlicz-Sobolev space associated with these equations, such as density results, continuous and compact embeddings. Moreover, we investigate the characteristics of the new anisotropic double phase operator, including its $(S^+)$ -property, strict monotonicity, and continuity. Furthermore, we establish the existence of at least one weak solution for our problem by using the surjectivity result for pseudomonotone operators. Additionally, under certain supplementary conditions on the data, we derive the uniqueness of the solution.

How to Cite this Article:
N. Chems Eddine, A. Ouannasser, M.A. Ragusa, On a new class of anisotropic double phase equations, J. Nonlinear Var. Anal. 9 (2025), 329-355.