关于高阶非线性微分方程的正解

Positive Solutions for Higher Order Nonlinear Differential Equations

在这篇论文中,通过使用Krasnosel'skii不动点理论和在适当的条件下,给出下面方程的一个和多个正解的存在:(-1)pu(2p)=λa(t)f(u(t),v(t)),t∈眼0,1演(-1)qv(2q)=μa(t)g(u(t),v(t)),t∈眼0,1演u(2i)(0)=u(2i+1)(1)=0,0≤i≤p-1,v(2j)(0)=v(2j+1)(1)=0,0≤j≤q-1,其中λ>0,μ>0,p,q∈N.

On the basis of Krasnosel'skii's fixed point theorem and under suitable conditions, the author presents the existence of single and multiple positive solutions to the following systems: (-1)p u(2p)=λa(t)f(u(t),v(t)), t∈[0,1](-1)q v(2q)= μa(t)g(u(t),v(t)), t∈[0,1]u(2i)(0)=u(2i+1)(1)=0, 0≤i≤p-1,v(2j)(0)=v(2j+1)(1)=0, 0≤j≤q-1, Where λ>0,μ>0,p,q∈N.