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| Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection* |
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Citation： |
Liting YOU,Huijuan SONG,Jingxue YIN.Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection*[J].Chinese Annals of Mathematics B,2022,43(5):643~658 |
| Page view： 409
Net amount： 417 |
Authors： |
Liting YOU; Huijuan SONG;Jingxue YIN |
Foundation： |
National Natural Science Foundation of China (Nos.12171166, 11601200, 11771156, 11861038, 12161045, 12026220). |
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| Abstract： |
In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|α|?u|p?2?u) + λ 1/|x|β |?u|p?2?u · x = |x|γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|α|?u|p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? RN(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection. |
Keywords： |
Weighted p-Laplacian, Multiplicity of solutions, Isolated singularities, Convection |
Classification： |
35J66, 35J75 |
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