<p>In this paper, we investigate the existence of weak solutions for a class of nonlinear double-phase operators with mixed growth. These operators involve a potential term and a gradient-dependent convection term, considered within the framework of Orlicz–Zygmund spaces. The analysis is based on the surjectivity result for pseudo-monotone operators. The findings presented here extend and generalize several well-known results.</p>

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Investigation into double-phase elliptic problems with boundary conditions, incorporating a logarithmic convection term

  • Ahmed El Ouardani,
  • Ahmed Aberqi,
  • Omar Benslimane,
  • Mhamed El Massoudi

摘要

In this paper, we investigate the existence of weak solutions for a class of nonlinear double-phase operators with mixed growth. These operators involve a potential term and a gradient-dependent convection term, considered within the framework of Orlicz–Zygmund spaces. The analysis is based on the surjectivity result for pseudo-monotone operators. The findings presented here extend and generalize several well-known results.