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On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces

  • Soufiane Kassimi EMAIL logo , Hajar Sabiki and Hicham Moussa
Published/Copyright: September 3, 2024
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Abstract

In this paper, we concern the existence result of the following general eigenvalue problem:

{ 𝒜 ( u ) = λ ( u ) in  Ω , D α ( u ) = 0 on  Ω ,

in an arbitrary Musielak–Orlicz spaces, where 𝒜 and are quasilinear operators in divergence form of order 2 n and 2 ( n - 1 ) , respectively. The main assumptions in this case are that 𝒜 and are potential operators with 𝒜 being elliptic and monotone. In this study, we intentionally avoid imposing constraints on the growth of a generalized N-function, including the Δ 2 -condition for both the generalized N-function and its conjugate. Consequently, this necessitates the formulation of the approximation theorem and the extensive utilization of modular convergence concepts.

MSC 2020: 35J60; 35P30; 46E30

Acknowledgements

The authors express sincere appreciation to the Editors and anonymous referees for their invaluable feedback and thoughtful recommendations, which have greatly enhanced the substance and quality of this paper.

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Received: 2024-02-18
Revised: 2024-04-02
Accepted: 2024-04-22
Published Online: 2024-09-03
Published in Print: 2025-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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