摘要:
研究了非线性四阶常微分方程(ordinary differential equation，简称ODE)边值问题
其中r是一个正参数，非线性f:[0,1]×[0,∞)×[0,∞)→[0,∞)项为连续函数，且存在常数满足a+b>0，c+d>0，使得当u→0时，f(t,u,p)=au+bp+(|(u,p)|)，当u→∞时，f(t,u,p)=cu+dp+o(|(u,p)|)，通过运用全局分歧理论，证明了该问题正解的存在性。
Abstract:
This article studies the boundary value problems of nonlinear fourth-order ordinary differential equations
where r is a positive parameter, nonlinearity f:[0,1]×[0,∞)×[0,∞)→[0,∞) is a continuous function, and there exist four constants satisfying a+b>0,c+d>0, so when u→0, f(t,u,p)=au+bp+(|(u,p)|); when u→∞, f(t,u,p)=cu+dp+o(|(u,p)|). The existence of positive solutions is obtained by using the global bifurcation theorem.