非线性方程的正解和正固有元

Positive Solutions and Positive Eigenelement for Nonlinear Equations

本文通过非线性算子 A 沿锥的导算子 A_+~′(θ)和 A_+~′(∞)的谱半径 p(A_+~′(θ))和 p(A_+~′(∞))的值,来判定 A 的不动点指数是否为0,从而判定 A 的正不动点和固有元的存在性,然后将这些抽象结果应用于 Hammerstein 积分方程和微分方程的两点边值问题,得到一些新的结果。

In this paper,first,we prove a result for determining fixed point index of a completely continuous nonlinear positive operator A,whet- her to become o or not,using the spectral radius ρA■(θ)) or ρA■(∞)) of the derived operator ρ(A■(θ)) or ρ(A■(∞)) of the operator A,and so obtain a some of existence theorems of postive solutions and positive eigenelements,second,we use these results to the Hammerstein integral equation and the two points boundary value problem of a differential equation,and so obtain a some of existence theorems of these peobewms.