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This paper is devoted to the study of a new kind of double-phase system with nearly bounded and critical growth. In particular, by exploiting a recent result on a new equivalence between the Luxemburg norm \(\Vert . \Vert _{L^{p} \log ^{\alpha } L \left( \Omega \right) }\) and the modular function \(\left[ . \right] _{L^{p} \log ^{\alpha } L \left( \Omega \right) }\) , we establish the existence of nontrivial weak solutions through the surjectivity result for pseudo-monotone operators. Our findings offer new insights into mathematical framework of such systems, paving the way for further advancements in the field.

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New Kind of Double Phase System with Nearly Bounded

  • 会议论文

  • 发表日期：

    2026年

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  • A. Aberqi,
  • O. Benslimane,
  • M. Elmassoudi,
  • A. El Ouardani

摘要

This paper is devoted to the study of a new kind of double-phase system with nearly bounded and critical growth. In particular, by exploiting a recent result on a new equivalence between the Luxemburg norm \(\Vert . \Vert _{L^{p} \log ^{\alpha } L \left( \Omega \right) }\) and the modular function \(\left[ . \right] _{L^{p} \log ^{\alpha } L \left( \Omega \right) }\) , we establish the existence of nontrivial weak solutions through the surjectivity result for pseudo-monotone operators. Our findings offer new insights into mathematical framework of such systems, paving the way for further advancements in the field.