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

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.