带参数的非线性简单支撑静态梁方程正解的存在性及多解性

Existence and Multiplicity of Positive Solutions for NonlinearSimply Supported Static Beam Equations with a Parameter

用上下解方法和拓扑度理论讨论带参数的非线性简单支撑静态梁方程y^(″″)(x)+(k 1+k 2)y^(″)(x)+k 1k 2y(x)=λf(x,y(x)),0<x<1,y(0)=y(1)=y″(0)=y″(1)=0正解的存在性和多解性,其中:λ>0是一个参数;k 1<k 2<0,k 1,k 2均为实常数;f:[0,1]×[0,∞)→(0,∞)为连续函数,且f(x,y)对固定的x∈[0,1]关于y单调增.

By using the methods of upper and lower solutions and topological degree theory,the author discusses the existence and multiplicity of positive solutions for the nonlinear simply supported static beam equations with a parameter y^(″″)(x)+(k 1+k 2)y^(″)(x)+k 1k 2y(x)=λf(x,y(x)),0<x<1,y(0)=y(1)=y^(″)(0)=y^(″)(1)=0,whereλ>0 is a parameter,k 1<k 2<0,k 1 and k 2 are real constants,f:[0,1]×[0,∞)→(0,∞)is a continuous function,and f(x,y)monotonically increases with respect to y for a fixed x∈[0,1].