POSITIVE SOLUTIONS TO SECOND-ORDER SINGULAR NEUMANN BOUNDARY VALUE PROBLEM WITH PARAMETERS IN THE BOUNDARY CONDITIONS  

作　　者：Zhilong Li (School of Informational Management, Jiangxi University of Finance and Economics, Nanchang 330013) 

出　　处：《Annals of Differential Equations》2009年第4期407-413,共7页微分方程年刊（英文版）

基　　金：Supported by NNSF of China (No.60665001);Educational Department of Jiangxi Province(No.GJJ08358, No.GJJ08359, No.JXJG07436)

摘　　要：In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.

关 键 词：fixed point index lower and upper solutions method Neumann boundary value problem positive solutions spectral radius of linear operators 

分 类 号：O175.8[理学—数学]