Existence of solutions to nonlinear problems with three-point boundary conditions

Abstract

Using Leray-Schauder degree theory and the method of upper and lower solutions, we obtain a solution for nonlinear boundary-value problem $$\displaylines{ \big(\varphi(u' )\big)'= f(t,u,u') \cr l(u,u')=0, }$$ where l(u,u')=0 denotes the three-point boundary conditions on [0,T], and $\varphi$ is a homeomorphism such that $\varphi(0)=0$.

Keywords

• Boundary value problems
• Schauder fixed point theorem
• Leray-Schauder degree
• lower and upper solutions