School of Mathematics and Statistics， Northwest Normal University， Lanzhou 730070， China）The existence and multiplicity of positive radial solutions for a class of p-Laplacian problems(一类p-Laplacian问题正径向解的存在性与多解性)

Abstract

We consider the following class of p-Laplacian problemwhere 11,x∈RN,u(x)=b, | x |=1,u(x)→a, | x |→+∞,（P）(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∈Lloc1（（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。)

Keywords

• p-laplacian problem(p-laplacian问题)
• multiplicity(多解性)
• upper and lower solutions(上下解)
• topological degree(拓扑度)