A monotone iterative technique for solving the bending elastic beam equations

摘要

This paper discusses the solvability of the fourth-order boundary value problemu(4)=f(t,u,u″),0⩽t⩽1,u(0)=u(1)=u″(0)=u″(1)=0,which models a statically bending elastic beam whose two ends are simply supported, where f:[0,1]×R2→R is continuous. We build a maximum principle for the corresponding linear equation. Using this maximum principle, we develop a monotone iterative technique in the presence of lower and upper solutions to solve the nonlinear equation and obtain some existence and uniqueness results.