非正非线性算子方程正解的存在性及其应用

Positive Solutions of Non-Positone Nonlinear Operator Equations and Its Applications

首先使用全局分歧理论得到了含参数非线性算子方程解集无界连通分支存在的结果,然后根据算子的正连通性得到了一类非正非线性算子方程正解的存在结果.使用本文的主要结果在无需假设非线性项为正的条件下可以得到某些微分边值问题正解的存在结果.

In this paper,firstly some existence results for unbounded connected component of solutions set of some nonlinear operator equations with parameter be obtained by using the global bifurcation theories,and then some existence results for positive solutions of a non-positone operator equation be obtained by using the positive connected property of the operator.The main results can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinear terms are positone.