Quadratic Singular Perturbation Problems With Nonmonotone Transition Layer Properties

In this article, we consider the quadratic singular perturbation problems with Nonmonotone Transition Layer Properties. Under certain conditions, solutions are shown to exhibit nonmonotone transition layer behavior at turning point t=0. The formal approximation of problems is constructed using composite expansions, and then approximation solutions of left and right sides at t=0 are joined by joint method which exhibits spike layer behavior and boundary layer behavior respectively. As a result, an approximate solution is formed which exhibits nonmonotone transition layer behavior. In addition, the existence and asymptotic behavior of solutions are proved by the theory of differential inequalities.