New results of some existence theorems on nonlinear boundary value problems

Abstract

With the use of the homeomorphism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, which generalizes results of Brown. When our results are applied to the existence and uniqueness of periodic solutions for nonlinear perturbed conservative systems ( Newtonian equations of motion), the existence and uniqueness of the solution are obtained. The results in this note seem less restrictive than those of the former papers we have seen. Meanwhile, as far as we know, it seems that applying the homeomorphism theory to the research of this kind of problem is new.