Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs

Abstract

We are concerned with the following system of third-order three-point boundary value problems:u′′′(t)+f(t,v(t))=0,t∈(0,1),v′′′(t)+g(t,u(t))=0,t∈(0,1),u(0)=u′′(0)=0,u′(1)=αu(η),v(0)=v′′(0)=0, andv′(1)=αv(η), where0<η<1and0<α<1/η. By imposing some suitable conditions onfandg, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.