二阶非线性常微分方程组正解及多个正解的存在性

Existence and Multiplicity of Positive Solutions of Nonlinear Second Order Ordinary Differential Systems

讨论二阶非线性常微分方程组边值问题的正解及多个正解的存在性.利用锥上算子不动点指数的同伦不变性 ,建立了问题正解的存在性 ,突破了以往文献要求非线性项在零点或无穷远点超线性或次线性增长的限制.

The paper is concerned with the existence and multiplicity of positive solutions of nonlinear second order ordi-nary differential systems of boundary value problems.The existence of positive solutions for the problem is established by using homotopy invariance of fixed point index in a cone,which do not require that the nonlinear terms are superlinear or sublinear at ends(zero or infinity).