n阶非线性两点奇异边值问题单调正解的存在性

The existence of monotone positive solutions for singular nonlinear nth-order two-point boundary problems

利用锥拉伸与压缩不动点定理,讨论n阶奇异边值问题{x(n)(t)+λα(t)f(t,x(t))=0,t∈(a,b),x(a)=x″(a)=…=x(n-1)(a)=0,x′(b)=0非减正解的存在性,其中λ>0是常数,α∈C((a,b),R+),f∈C([a,b]×(0,∞),R+),R+是正实数集,α(t)可以在t=a,b处奇异,f(t,s)可以在s=0处奇异.

In this paper,the existence of positive solutions is studied for the following singular nonlinear nth-order two-point boundary problems:x(n)(t)+λα(t)f(t,x(t))=0,t∈(a,b),x(a)=x″(a)=…=x(n-1)(a)=0,x′(b)=0,where λ>0 is a constant,α∈C((a,b),RBX+),f∈C(×(0,∞),RBX+),RBX+ is the positive real set,α(t) may be singular at t=a,b and f(t,s) may be singular at s=0.