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| Monotonicity and Symmetry of Positive Solutions to Logarithmic LaplacianEquations and Systems with Gradient Terms |
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Citation： |
Xianghui XU ·,Tingzhi CHENG.Monotonicity and Symmetry of Positive Solutions to Logarithmic LaplacianEquations and Systems with Gradient Terms[J].Chinese Annals of Mathematics B,2026,(5):823~832 |
| Page view： 2
Net amount： 8 |
Authors： |
Xianghui XU ·; Tingzhi CHENG |
Foundation： |
the National Natural Science Foundation of China (Nos. 12501263,
12401259), the Shandong Provincial Natural Science Foundation (No. ZR2021QA070) and the Shanghai
Frontier Research Center of Modern Analysis. |
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| Abstract： |
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. |
Keywords： |
Logarithmic Laplacian Monotonicity Positive solution Convex domain |
Classification： |
35J67, 35R11 |
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