Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection

作     者：Liting YOU Huijuan SONG Jingxue YIN Liting YOU;Huijuan SONG;Jingxue YIN

作者机构：School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510631China School of Mathematics and StatisticsJiangxi Normal UniversityNanchang 330022China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2022年第43卷第5期

页      面：643-658页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.12171166 11601200 11771156 11861038 12161045 12026220) 

主　　题：Weighted p-Laplacian Multiplicity of solutions Isolated singularities Convection 

摘      要：In this paper,the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and diffusion suppressed by convection-div(|x|^(α)|■u|^(p-2)■u)+λ^(1)/|x|β|■u|^(p-2)■u·x=|x|^(γ)g(|x|)in B{0}subject to nonlinear Robin boundary value condition|x|^(α)|■u|^(p-2)■u·n=A-ρu on■B,whereλ0,B■RN(N≥2)is the unit ball centered at the origin,α0,p1,β∈R,γ-N,g∈C(0,1])with g(0)0,A∈R,ρ0 and n is the unit outward *** same problem with diffusion promoted by convection,namely λ≤0,has already been discussed by the last two authors(Song-Yin(2012)),where the existence,nonexistence and classification of singularities for solutions are *** different from[Song,*** Yin,J.X.,Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection,***.,35,2012,1089-1100],in the present caseλ0,namely the diffusion is suppressed by the convection,non-singular solutions are not only existent but also may be infinite which vary according only to the values of solutions at the isolated singular *** the same time,the singular solutions may exist only if the diffusion dominates the convection.