三阶非线性特征值问题解的存在性

Existence of Non-negative Solutions of Nonlinear Third order Eigenvalue Problems

利用锥不动点指数研究了三阶非线性特征值问题u+ρ3u=λg(t)f(u),0<t<2π,u(i)(0)=u(i)(2π),i=0,1,2在适当条件下解的存在性.其中常数ρ∈0,13,参数λ>0.

The authors consider the nonlinear third order differential equations u^n＋p^3u=λg（t）f（u）,0〈t〈2π with the periodic boundary conditions u^（i）（0）=u^（i）（2π）,i=0,1,2 Where ρ∈（0,1/√3） is a constant, λ〉 0 is a parameter, Two results on the existence of nonnegative solutions to problem （B）-（E） are obtained. And the proof uses the fixed point ndex in the cone theory,