非线性三阶差分方程三点特征值问题的正解

Positive Solutions to Three-Point Eigenalue Problems for Nonlinear Third-Order Difference Equations

摘要:

在本文中,通过使用锥不动点定理,我们得到离散非线性三阶三点特征值问题的正解的存在 △3u(t-1)= λa(t)f(t,u(t)),t∈[1,T]Z, u(0)=△u(ƞ)=△u(T)=0, 这里 ƞ∈[[(T2+T)/(3T+2)]+1,T]Z,和λ>0 是一个参数.

Abstract:

In this paper, by using the fixed point theorem in cone, we obtain the existence of positive solutions to the discrete nonlinear third-order three-point eigenvalue problem △3u(t-1)= λa(t)f(t,u(t)),t∈[1,T]Z, u(0)=△u(ƞ)=△u(T)=0, where ƞ∈[[(T2+T)/(3T+2)]+1,T]Z, and λ>0 is a parameter.