Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài :Delayed phenomenon of loss of stability of solutions in a second-order quasi-linear singularly perturbed boundary value problem with a turning point | Zhou and Shen Boundary Value Problems 2011 2011 35 http content 2011 1 35 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Delayed phenomenon of loss of stability of solutions in a second-order quasi-linear singularly perturbed boundary value problem with a turning point Zheyan Zhou and Jianhe Shen Correspondence zzy@ School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 People s Republic of China Springer Abstract Based on the method of differential inequalities by constructing the upper ad lower solutions suitably delayed phenomenon of loss of stability of solutions in a second-order quasi-linear singularly perturbed Dirichlet boundary value problem with a turning point is found in this paper. An illustrating example is performed to verify the obtained results. Keywords Upper and lower solutions singular perturbation turning point delay of loss of stability 1 Introduction In real-world applications there are numerous examples from biology chemistry neurophysiology fluid dynamics automation semiconductor laser etc. are described in dynamical systems with singular perturbation. The process evolving more than one scale in time and or space is a typical feature of such type of dynamical systems. The studies of singular perturbation can be traced back to nineteenth century stimulated greatly by celestial mechanics at that time. The Lindstedt-Poincaré method could be regarded as the first invention to deal with the secular term problems which is one of the two broad categories of singularly perturbed problems 1 2 . Another broad category of singularly perturbed problems is the boundary layer problems 1 2 . The idea of boundary layer was proposed by Prandtl in the setting of fluid dynamics and aerodynamics. Matching principle was an invention of Prandtl to obtain uniformly valid asymptotic solutions of boundary layer problems. In the process of developing the theory of singular .
