一类p-Laplacian问题正径向解的存在性与多解性OA北大核心CSTPCD
The existence and multiplicity of positive radial solutions for a class of p-Laplacian problems
研究了p-Laplacian问题{-div(| ∇u | p-2∇u)=q(| x |)f(u),| x |>1,x∈RN,u(x)=b,| x |= 1,u(x)→a,| x |→+∞,其中,1<p<N,a,b为正参数,q∈L1loc((1,+∞),[0,+∞)),f∈C([0,+∞),[0,+∞)).运用锥上的不动点定理、上下解方法和拓扑度理论,获得了p-Laplacian问题正解的存在性和多解性结果.
We consider the following class of p-Laplacian problem{-div(| ∇u | p-2∇u)=q(| x |)f(u),| x |>1,x∈RN,u(x)=b,| x |= 1,u(x)→a,| x |→+∞,(P)where 1<p<N,a,b are positive parameters,q∈L1loc((1,+∞),[0,+∞)),f∈C([0,+∞),[0,+∞)).By apply-ing the fixed point theorem in cones,the method of upper and lower solutions and topological degree theory,we obtain the existence and multiplicity of positive solutions for the above p-Laplacian problem.
石轩荣
西北师范大学 数学与统计学院,甘肃 兰州 730070
数学
p-Laplacian问题多解性上下解拓扑度
p-Laplacian problemmultiplicityupper and lower solutionstopological degree
《浙江大学学报（理学版）》 2024 (003)
277-281 / 5
国家自然科学基金资助项目(12061064).
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