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<p>This paper is concerned with logarithmic Laplacian equations and systems with gradient terms in bounded convex domains. Under some assumptions on the nonlinearities, the authors prove the strict monotonicity and symmetry of positive solutions. In particular, the authors establish one new estimate of the logarithmic Laplacian operator that plays an important role in applying the direct method of moving planes. This paper seems to be the first one to deal with the monotonicity and symmetry of positive solutions to logarithmic Laplacian equations and systems with gradient terms.</p>

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Monotonicity and Symmetry of Positive Solutions to Logarithmic Laplacian Equations and Systems with Gradient Terms

  • 期刊论文

  • 发表日期：

    2026年6月24日

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  • Xianghui Xu,
  • Tingzhi Cheng

摘要

This paper is concerned with logarithmic Laplacian equations and systems with gradient terms in bounded convex domains. Under some assumptions on the nonlinearities, the authors prove the strict monotonicity and symmetry of positive solutions. In particular, the authors establish one new estimate of the logarithmic Laplacian operator that plays an important role in applying the direct method of moving planes. This paper seems to be the first one to deal with the monotonicity and symmetry of positive solutions to logarithmic Laplacian equations and systems with gradient terms.