一类p-Laplacian问题正径向解的存在性与多解性

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∈R^(N),u(x)=b,|x|=1,u(x)→a,|x|→+∞,其中,1<p<N,a,b为正参数,q∈L^(1)_(loc)((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∈R^(N),u(x)=b,|x|=1,u(x)→a,|x|→+∞,(P)where 1<p<N,a,b are positive parameters,q∈L^(1)_(loc)((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.