Variational analysis of Kirchhoff equations in Musielak-Orlicz-Zygmund spaces

Ahmed El Ouardani; Ahmed Aberqi; Mhamed Elmassoudi

doi:10.24193/subbmath.2026.2.09

Authors

Ahmed El Ouardani LSATE Laboratory, ENSA, Sidi Mohamed Ben Abdellah University, Fez, Morocco
Ahmed Aberqi LSATE Laboratory, ENSA, Sidi Mohamed Ben Abdellah University, Fez, Morocco https://orcid.org/0000-0003-3599-9099
Mhamed Elmassoudi LSATE Laboratory, ENSA, Sidi Mohamed Ben Abdellah University, Fez, Morocco https://orcid.org/0000-0001-9335-9271

DOI:

https://doi.org/10.24193/subbmath.2026.2.09

Keywords:

Kirchhoff equations, double-phase problem, Musielak-Orlicz-Zygmund spaces, weak solutions, variational approaches

Abstract

We study a class of nonlocal Kirchhoff problems with nonlinearities exhibiting nonstandard growth. Using variational methods in Musielak-Orlicz-Zygmund spaces, we prove the existence of nontrivial weak solutions. The analysis uses generalized N-functions, Orlicz-Zygmund embeddings, pseudo-monotone operators, and the Palais-Smale condition, which allow handling double-phase and nonlocal Kirchhoff terms. The results extend classical variational methods to settings with borderline and logarithmic growth.

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